{"id":2265,"date":"2020-08-21T19:42:41","date_gmt":"2020-08-21T23:42:41","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/factor-quadratic-trinomials-with-leading-coefficient-1\/"},"modified":"2025-09-22T19:26:25","modified_gmt":"2025-09-22T23:26:25","slug":"factor-quadratic-trinomials-with-leading-coefficient-1","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/factor-quadratic-trinomials-with-leading-coefficient-1\/","title":{"raw":"8.5  Factor Quadratic Trinomials with Leading Coefficient 1","rendered":"8.5  Factor Quadratic Trinomials with Leading Coefficient 1"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Factor trinomials of the form \\({x}^{2}+bx+c\\)<\/li>\n \t<li>Factor trinomials of the form \\({x}^{2}+bxy+c{y}^{2}\\)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em> + <em data-effect=\"italics\">c<\/em><\/h1>\n<p id=\"fs-id1168344295319\">You have already learned how to multiply binomials using FOIL. Now you\u2019ll need to \u201cundo\u201d this multiplication\u2014to start with the product and end up with the factors. Let\u2019s look at an example of multiplying binomials to refresh your memory.<\/p>\n<span id=\"fs-id1168344504686\" data-type=\"media\" data-alt=\"This figure shows the steps of multiplying the factors (x + 2) times (x + 3). The multiplying is completed using FOIL to demonstrate. The first term is x squared and is below F. The second term is 3 x below \u201cO\u201d. The third term is 2 x below \u201cI\u201d. The fourth term is 6 below L. The simplified product is then given as x 2 plus 5 x + 6.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_Elem20Alg_Figure_07_02_001_img_new.jpg\" alt=\"This figure shows the steps of multiplying the factors (x + 2) times (x + 3). The multiplying is completed using FOIL to demonstrate. The first term is x squared and is below F. The second term is 3 x below \u201cO\u201d. The third term is 2 x below \u201cI\u201d. The fourth term is 6 below L. The simplified product is then given as x 2 plus 5 x + 6.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1168343053818\">To factor the trinomial means to start with the product, \\({x}^{2}+5x+6\\), and end with the factors, \\(\\left(x+2\\right)\\left(x+3\\right)\\). You need to think about where each of the terms in the trinomial came from.<\/p>\n<p id=\"fs-id1168343004832\">The <em data-effect=\"italics\">first term<\/em> came from multiplying the first term in each binomial. So to get \\({x}^{2}\\) in the product, each binomial must start with an <em data-effect=\"italics\">x<\/em>.<\/p>\n\n<div id=\"fs-id1168344112344\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}{x}^{2}+5x+6\\\\ \\left(x\\right)\\left(x\\right)\\end{array}\\)<\/div>\n<p id=\"fs-id1168344149571\">The <em data-effect=\"italics\">last term<\/em> in the trinomial came from multiplying the last term in each binomial. So the last terms must multiply to 6<\/p>\n<p id=\"fs-id1168344335725\">What two numbers multiply to 6?<\/p>\n<p id=\"fs-id1168343239771\">The factors of 6 could be 1 and 6, or 2 and 3. How do you know which pair to use?<\/p>\n<p id=\"fs-id1168344516045\">Consider the <em data-effect=\"italics\">middle term<\/em>. It came from adding the outer and inner terms.<\/p>\n<p id=\"fs-id1168343129934\">So the numbers that must have a product of 6 will need a sum of 5. We\u2019ll test both possibilities and summarize the results in the table below\u2014the table will be very helpful when you work with numbers that can be factored in many different ways.<\/p>\n\n<table id=\"fs-id1168344555789\" class=\"grid\" summary=\"This table consists of two columns and 3 rows. The first row of the first column reads \u201cFactors od 6.\u201d The next row down includes the factors 1, 6. The third row includes the factors 2, 3. The second column head reads \u201csum of factors.\u201d The next row under this reads 1 plus 6 equals 7. The next row down reads 2 plus 3 equals 5.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(6\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(1,6\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+6=7\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(2,3\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(2+3=5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344368014\">We see that 2 and 3 are the numbers that multiply to 6 and add to 5. So we have the factors of \\({x}^{2}+5x+6\\). They are \\(\\left(x+2\\right)\\left(x+3\\right)\\).<\/p>\n\n<div id=\"fs-id1168344111440\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ll}{x}^{2}+5x+6 \\qquad \\quad&amp;\u00a0 \\text{product}\\\\ \\left(x+2\\right)\\left(x+3\\right)\\qquad \\quad &amp; \\text{factors}\\end{array}\\)<\/div>\n<p id=\"fs-id1168344120416\">You should check this by multiplying.<\/p>\n<p id=\"fs-id1168344332394\">Looking back, we started with \\({x}^{2}+5x+6\\), which is of the form \\({x}^{2}+bx+c\\), where \\(b=5\\) and \\(c=6\\). We factored it into two binomials of the form \\(\\left(x+m\\right)\\) and \\(\\left(x+n\\right)\\).<\/p>\n\n<div id=\"fs-id1168344306410\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cc}{x}^{2}+5x+6\\qquad \\quad &amp; {x}^{2}+bx+c\\\\ \\left(x+2\\right)\\left(x+3\\right)\\qquad \\quad&amp; \\left(x+m\\right)\\left(x+n\\right)\\end{array}\\)<\/div>\n<p id=\"fs-id1168344104178\">To get the correct factors, we found two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> whose product is <em data-effect=\"italics\">c<\/em> and sum is <em data-effect=\"italics\">b<\/em>.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Factor Trinomials of the Form \\({x}^{2}+bx+c\\)<\/div>\n<div id=\"fs-id1168343096854\" data-type=\"exercise\">\n<div id=\"fs-id1168344202406\" data-type=\"problem\">\n<p id=\"fs-id1168343007559\">Factor: \\({x}^{2}+7x+12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343188796\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<span id=\"fs-id1168343052084\" data-type=\"media\" data-alt=\"This table gives the steps for factoring x squared + 7 x + 12. The first row states the first step \u201cwrite the factors as two binomials with first terms x\u201d. In the second column of the first row it states, \u201cwrite two sets of parentheses and put x as the first term\u201d. In the third column, it has the expression x squared + 7 x +12. Below the expression are two sets of parentheses with x as the first term.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002a_img_new.jpg\" alt=\"This table gives the steps for factoring x squared + 7 x + 12. The first row states the first step \u201cwrite the factors as two binomials with first terms x\u201d. In the second column of the first row it states, \u201cwrite two sets of parentheses and put x as the first term\u201d. In the third column, it has the expression x squared + 7 x +12. Below the expression are two sets of parentheses with x as the first term.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168344116515\" data-type=\"media\" data-alt=\"The second row states the second step \u201cfind two numbers m and n that multiply to c, m times n = c and add to b, m + n = b\u201d. In the second column of the second row are the factors of 12 and their sums. 1,12 with sum 1 + 12 = 13. 2, 6 with sum 2 + 6 =8. 3, 4 with sum 3 + 4 = 7.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002b_img_new.jpg\" alt=\"The second row states the second step \u201cfind two numbers m and n that multiply to c, m times n = c and add to b, m + n = b\u201d. In the second column of the second row are the factors of 12 and their sums. 1,12 with sum 1 + 12 = 13. 2, 6 with sum 2 + 6 =8. 3, 4 with sum 3 + 4 = 7.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168344084942\" data-type=\"media\" data-alt=\"The third row states \u201cuse m and n as the last terms of the factors\u201d. The second column states \u201cuse 3 and 4 as the last terms of the binomials\u201d. The third column in this row has the product (x + 3)(x + 4).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002c_img_new.jpg\" alt=\"The third row states \u201cuse m and n as the last terms of the factors\u201d. The second column states \u201cuse 3 and 4 as the last terms of the binomials\u201d. The third column in this row has the product (x + 3)(x + 4).\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168344441086\" data-type=\"media\" data-alt=\"In the fourth row the statement is \u201ccheck by multiplying the factors\u201d. The product of (x + 3)(x +4) is shown to be x 2 + 7 x + 12.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002d_img_new.jpg\" alt=\"In the fourth row the statement is \u201ccheck by multiplying the factors\u201d. The product of (x + 3)(x +4) is shown to be x 2 + 7 x + 12.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344080907\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344075573\" data-type=\"exercise\">\n<div id=\"fs-id1168344228715\" data-type=\"problem\">\n<p id=\"fs-id1168343160986\">Factor: \\({x}^{2}+6x+8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344075926\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344318972\">\\(\\left(x+2\\right)\\left(x+4\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344316847\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344343972\" data-type=\"exercise\">\n<div id=\"fs-id1168344285818\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1168344249495\" data-type=\"solution\">\n<p id=\"fs-id1168344370815\"><\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285818\" data-type=\"problem\">\n<p id=\"fs-id1168343113310\">Factor: \\({y}^{2}+8y+15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344249495\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344370815\">\\(\\left(y+3\\right)\\left(y+5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344254623\">Let\u2019s summarize the steps we used to find the factors.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO:<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n\nFactor trinomials of the form \\({x}^{2}+bx+c\\).\n<ol id=\"fs-id1168744022333\" class=\"stepwise\" type=\"1\">\n \t<li>Write the factors as two binomials with first terms <em data-effect=\"italics\">x<\/em>: \\((x)(x)\\).<\/li>\n \t<li>Find two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> that\nMultiply to <em data-effect=\"italics\">c<\/em>, \\(m\\cdot n=c\\)\nAdd to <em data-effect=\"italics\">b<\/em>, \\(m+n=b\\)<\/li>\n \t<li>Use <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> as the last terms of the factors: \\(\\left(x+m\\right)\\left(x+n\\right)\\).<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344193768\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343140469\" data-type=\"problem\">\n<p id=\"fs-id1168343174220\">Factor: \\({u}^{2}+11u+24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344074028\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343062758\">Notice that the variable is <em data-effect=\"italics\">u<\/em>, so the factors will have first terms <em data-effect=\"italics\">u<\/em>.<\/p>\n<p id=\"fs-id1168344330736\">\\(\\begin{array}{cc}&amp;\u00a0 {u}^{2}+11u+24\\\\ \\text{Write the factors as two binomials with first terms u.} &amp; \\left(u\\right)\\left(u\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168344320345\">Find two numbers that: multiply to 24 and add to 11<\/p>\n\n<table id=\"fs-id1168343095225\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 24 and the second column is labeled sum of the factors. The first row is 1, 24 with sum in the second column 1 + 24 = 25. The second row is 2, 12 with sum 2 + 12 = 14. The third row is 3,8 with sum 3 + 8 = 11. The fourth row is 4,6 with sum 4 + 6 = 10.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Factors of \\(24\\)<\/th>\n<th data-valign=\"middle\" data-align=\"center\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(1,24\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+24=25\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(2,12\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(2+12=14\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(3,8\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(3+8=11\\text{*}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(4,6\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(4+6=10\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344218997\">Use 3 and 8 as the last terms of the binomials.\u00a0 \\(\\left(u+3\\right)\\left(u+8\\right)\\)<\/p>\nCheck.\n\n\\(\\begin{array}{c}\\left(u+3\\right)\\left(u+8\\right) \\\\{u}^{2}+3u+8u+24 \\\\{u}^{2}+11u+24\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFactor: \\({q}^{2}+10q+24\\).\n<div id=\"fs-id1168344327546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343004687\" data-type=\"exercise\">\n<div id=\"fs-id1168343054538\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343130483\">\\(\\left(q+4\\right)\\left(q+6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343097190\" data-type=\"problem\">\n<p id=\"fs-id1168343097192\">Factor: \\({t}^{2}+14t+24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344303612\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344254324\">\\(\\left(t+2\\right)\\left(t+12\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344327546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343004687\" data-type=\"exercise\">\n<div id=\"fs-id1168343004689\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344602096\" data-type=\"problem\">\n<p id=\"fs-id1168344602098\">Factor: \\({y}^{2}+17y+60\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344309961\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343060258\">\\(\\begin{array}{cc}&amp; {y}^{2}+17y+60\\\\ \\text{Write the factors as two binomials with first terms y.} &amp; \\left(y\\right)\\left(y\\right)\\hfill \\end{array}\\)<\/p>\n<p id=\"fs-id1168343187961\">Find two numbers that multiply to 60 and add to 17<\/p>\n\n<table id=\"fs-id1168344371538\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 60 and the second column is labeled sum of factors. The first row has 1, 60 with sum 1 + 60 = 61. The second row has 2, 30 with sum 2 + 30 = 32. The third row has 3, 20 with sum 3 + 20 = 23. The fourth row has 4, 15 with sum 4 + 15 = 19. The fifth row has 5, 12 with sum 5 + 12 = 17 (this has an asterisk). The last row has 6,10 with sum 6 + 10 = 16.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(60\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(1,60\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+60=61\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(2,30\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(2+30=32\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(3,20\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(3+20=23\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(4,15\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(4+15=19\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(5,12\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(5+12=17\\text{*}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(6,10\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(6+10=16\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344593946\">Use 5 and 12 as the last terms.\u00a0 \u00a0 \u00a0\\(\\left(y+5\\right)\\left(y+12\\right)\\)<\/p>\nCheck.\n\n\\(\\begin{array}{c}(y+5)(y+12) \\\\ ({y}^{2}+12y+5y+60) \\\\({y}^{2}+17y+60)\\checkmark\\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343070207\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344315968\" data-type=\"exercise\">\n<div id=\"fs-id1168344303612\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344108342\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344438118\" data-type=\"exercise\">\n<div id=\"fs-id1168344438120\" data-type=\"problem\">\n<p id=\"fs-id1168344438122\">Factor: \\({x}^{2}+19x+60\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343244794\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343244796\">\\(\\left(x+4\\right)\\left(x+15\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343046948\" data-type=\"problem\">\n<p id=\"fs-id1168343070859\">Factor: \\({v}^{2}+23v+60\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344592817\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344592819\">\\(\\left(v+3\\right)\\left(v+20\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em>\u00a0+ <em data-effect=\"italics\">c <\/em>with <em data-effect=\"italics\">b<\/em> Negative, <em data-effect=\"italics\">c<\/em> Positive<\/h1>\n<p id=\"fs-id1168344299853\">In the examples so far, all terms in the trinomial were positive. What happens when there are negative terms? Well, it depends which term is negative. Let\u2019s look first at trinomials with only the middle term negative.<\/p>\n<p id=\"fs-id1168344299856\">Remember: To get a negative sum and a positive product, the numbers must both be negative.<\/p>\n<p id=\"fs-id1168343096498\">Again, think about FOIL and where each term in the trinomial came from. Just as before,<\/p>\n\n<ul id=\"fs-id1168343096501\" data-bullet-style=\"bullet\">\n \t<li>the first term, \\({x}^{2}\\), comes from the product of the two first terms in each binomial factor, <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>;<\/li>\n \t<li>the positive last term is the product of the two last terms<\/li>\n \t<li>the negative middle term is the sum of the outer and inner terms.<\/li>\n<\/ul>\n<p id=\"fs-id1168342965159\">How do you get a <em data-effect=\"italics\">positive product<\/em> and a <em data-effect=\"italics\">negative sum<\/em>? With two negative numbers.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344108782\" data-type=\"problem\">\n<p id=\"fs-id1168343062436\">Factor: \\({t}^{2}-11t+28\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343239283\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344503443\">Again, with the positive last term, 28, and the negative middle term, \\(-11t\\), we need two negative factors. Find two numbers that multiply 28 and add to \\(-11\\).<\/p>\n<p id=\"fs-id1168344296828\">\\(\\begin{array}{cc} &amp; {t}^{2}-11t+28 \\\\ \\text{Write the factors as two binomials with first terms t.} &amp; \\left(t\\right)\\left(t\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168343045607\">Find two numbers that: multiply to 28 and add to \\(-11\\).<\/p>\n\n<table id=\"fs-id1168344106593\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 28 and the second column is labeled sum of factors. The first row has the factors negative 1, negative 28 and the sum negative 1 plus 9 minus 28) = negative 29. The second row has the factors negative 2, negative 14 and the sum negative 2 + (negative 14) = negative 16. The third row has the factors negative 4, negative 7 and the sum negative 4 + (negative 7) = negative 11. This one has an asterisk.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(28\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(-1,-28\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(-1+\\left(-28\\right)=-29\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(-2,-14\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(-2+\\left(-14\\right)=-16\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(-4,-7\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(-4+\\left(-7\\right)=-11\\text{*}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343060797\">Use -4, -7 as the last terms of the binomials.\u00a0 \u00a0 \\(\\left(t-4\\right)\\left(t-7\\right)\\)<\/p>\nCheck.\n\n\\(\\begin{array}{c}\\left(t-4\\right)\\left(t-7\\right) \\\\{t}^{2}-7t-4t+28\\\\{t}^{2}-11t+28\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343035188\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343035191\" data-type=\"exercise\">\n<div id=\"fs-id1168343190090\" data-type=\"problem\">\n<p id=\"fs-id1168343190092\">Factor: \\({u}^{2}-9u+18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344363425\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344363427\">\\(\\left(u-3\\right)\\left(u-6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343061523\" data-type=\"problem\">\n<p id=\"fs-id1168343061525\">Factor: \\({y}^{2}-16y+63\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343072480\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343072482\">\\(\\left(y-7\\right)\\left(y-9\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em>\u00a0+ <em data-effect=\"italics\">c <\/em>with <em data-effect=\"italics\">c<\/em> Negative<\/h1>\n<p id=\"fs-id1168344394803\">Now, what if the last term in the trinomial is negative? Think about FOIL. The last term is the product of the last terms in the two binomials. A negative product results from multiplying two numbers with opposite signs. You have to be very careful to choose factors to make sure you get the correct sign for the middle term, too.<\/p>\n<p id=\"fs-id1168344357952\">Remember: To get a negative product, the numbers must have different signs.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344317637\" data-type=\"problem\">\n<p id=\"fs-id1168344317639\">Factor: \\({z}^{2}+4z-5\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344074937\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343052674\">To get a negative last term, multiply one positive and one negative. We need factors of \\(-5\\) that add to positive 4<\/p>\n\n<table id=\"fs-id1168343062206\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of negative 5 and the second column is labeled sum of factors. The first row has the factors 1, negative 5 and the sum 1 + (negative 5) = negative 4. The second row has the factors negative 1, 5 and the sum negative 1 + 5 = 4.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(-5\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(1,-5\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+\\left(-5\\right)=-4\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(-1,5\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(-1+5=4\\text{*}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343008142\">Notice: We listed both \\(1,-5\\) and \\(-1,5\\) to make sure we got the sign of the middle term correct.<\/p>\n<p id=\"fs-id1168344336620\">\\(\\begin{array}{lc} &amp; {z}^{2}+4z-5\\\\ \\text{Factors will be two binomials with first terms z.} &amp; \\left(z\\right)\\left(z\\right)\\\\ \\text{Use -1, 5 as the last terms of the binomials.} &amp; \\left(z-1\\right)\\left(z+5\\right)\\end{array}\\)<\/p>\nCheck.\n\n\\(\\begin{array}{c}\\left(z-1\\right)\\left(z+5\\right)\\\\ {z}^{2}+5z-1z-5 \\\\ {z}^{2}+4z-5\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344199736\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344199740\" data-type=\"exercise\">\n<div id=\"fs-id1168344299180\" data-type=\"problem\">\n<p id=\"fs-id1168344299182\">Factor: \\({h}^{2}+4h-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343244524\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343244526\">\\(\\left(h-2\\right)\\left(h+6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343244830\" data-type=\"problem\">\n<p id=\"fs-id1168343244833\">Factor: \\({k}^{2}+k-20\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344440923\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344440925\">\\(\\left(k-4\\right)\\left(k+5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344215499\">Let\u2019s make a minor change to the last trinomial and see what effect it has on the factors.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343247201\" data-type=\"problem\">\n<p id=\"fs-id1168344282144\">Factor: \\({z}^{2}-4z-5\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344314789\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343046964\">This time, we need factors of \\(-5\\) that add to \\(-4\\).<\/p>\n\n<table id=\"fs-id1168343195050\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u22125 and the second column is labeled sum of factors. The first row has the factors 1, negative 5 and the sum 1 + (negative 5) = negative 4. This row has an asterisk. The second row has the factors negative 1, 5 and the sum negative 1 + 5 = 4.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(-5\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(1,-5\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+\\left(-5\\right)=-4\\text{*}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(-1,5\\)<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(-1+5=4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343003096\">\\(\\begin{array}{lc}&amp; {z}^{2}-4z-5\\\\ \\text{Factors will be two binomials with first terms z.} &amp; \\left(z\\right)\\left(z\\right)\\\\ \\text{Use 1, -5 as the last terms of the binomials.} &amp; \\left(z+1\\right)\\left(z-5\\right)\\end{array}\\)<\/p>\nCheck.\n\n\\(\\begin{array}{c}\\left(z+1\\right)\\left(z-5\\right) \\\\{z}^{2}-5z+1z-5 \\\\ {z}^{2}-4z-5\\checkmark \\end{array}\\)\n<p id=\"fs-id1168343047355\">Notice that the factors of \\({z}^{2}-4z-5\\) are very similar to the factors of \\({z}^{2}+4z-5\\). It is very important to make sure you choose the factor pair that results in the correct sign of the middle term.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344517387\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343053892\" data-type=\"exercise\">\n<div id=\"fs-id1168343053894\" data-type=\"problem\">\n<p id=\"fs-id1168343053896\">Factor: \\({x}^{2}-4x-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343052867\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343158900\">\\(\\left(x+2\\right)\\left(x-6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344424372\" data-type=\"problem\">\n<p id=\"fs-id1168344424374\">Factor: \\({y}^{2}-y-20\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344072690\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344072692\">\\(\\left(y+4\\right)\\left(y-5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342967370\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344424370\" data-type=\"exercise\">\n<div id=\"fs-id1168344072690\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343007276\" data-type=\"problem\">\n<p id=\"fs-id1168343238382\">Factor: \\({q}^{2}-2q-15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343024975\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343174963\">\\(\\begin{array}{cc} &amp; {q}^{2}-2q-15\\\\ \\text{Factors will be two binomials with first terms q.}&amp; \\left(q\\right)\\left(q\\right)\\\\ \\text{You can use 3, -5 as the last terms of the} &amp; \\left(q+3\\right)\\left(q-5\\right)\\\\ \\text{binomials.}&amp;\u00a0 \\end{array}\\)<\/p>\n\n<table id=\"fs-id1168344475602\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u221215 and the second column is labeled sum of factors. The first row has the factors 1, \u221215 and the sum 1 + (negative 15) = negative 14. The second row has the factors negative 1, 15 and the sum negative 1 + 15 = 14. The third row has the factors 3, negative 5 and the sum 3 + negative 5 = negative 2. This row has an asterisk. The fourth row has the factors negative 3, 5 and the sum negative 3 + 5 = 2.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(-15\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(1,-15\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(1+\\left(-15\\right)=-14\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-1,15\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-1+15=14\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(3,-5\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(3+\\left(-5\\right)=-2\\text{*}\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-3,5\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-3+5=2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168342964041\">Check.<\/p>\n<p id=\"fs-id1168343188574\">\\(\\left(q+3\\right)\\left(q-5\\right)\\)<\/p>\n<p id=\"fs-id1168343063093\">\\({q}^{2}-5q+3q-15\\)<\/p>\n<p id=\"fs-id1168342965730\">\\({q}^{2}-2q-15\\checkmark\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFactor: \\({r}^{2}-3r-40\\).\n<div id=\"fs-id1168343045190\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343045194\" data-type=\"exercise\">\n<div id=\"fs-id1168344076484\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343187780\">\\(\\left(r+5\\right)\\left(r-8\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342985416\" data-type=\"problem\">\n<p id=\"fs-id1168342985419\">Factor: \\({s}^{2}-3s-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343187846\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344120004\">\\(\\left(s+2\\right)\\left(s-5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168343175288\">Some trinomials are prime. The only way to be certain a trinomial is prime is to list all the possibilities and show that none of them work.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343053886\" data-type=\"problem\">\n<p id=\"fs-id1168343053889\">Factor: \\({y}^{2}-6y+15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343188057\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343188063\">\\(\\begin{array}{cc}&amp; {y}^{2}-6y+15\\\\ \\text{Factors will be two binomials with first} &amp; \\left(y\\right)\\left(y\\right)\\\\ \\text{terms y.} &amp; \\end{array}\\)<\/p>\n\n<table id=\"fs-id1168344294638\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 15 and the second column is labeled sum of factors. The first row has the factors negative 1, negative 15 and the sum negative 1 + (negative 15) = negative 16. The second row has the factors negative 3, negative 5 and the sum negative 3 + (negative 5) = negative 8.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of 15<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-1,-15\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-1+\\left(-15\\right)=-16\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-3,-5\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{0.4em}{0ex}}-3+\\left(-5\\right)=-8\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344520795\">As shown in the table, none of the factors add to \\(-6\\); therefore, the expression is prime.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344315809\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344441069\" data-type=\"exercise\">\n<div id=\"fs-id1168344441071\" data-type=\"problem\">\n<p id=\"fs-id1168344441073\">Factor: \\({m}^{2}+4m+18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343054990\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344108517\">prime<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343048175\" data-type=\"problem\">\n<p id=\"fs-id1168343048177\">Factor: \\({n}^{2}-10n+12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168342981700\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168342981702\">prime<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344108524\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344108527\" data-type=\"exercise\">\n<div id=\"fs-id1168342981700\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344310344\" data-type=\"problem\">\n<p id=\"fs-id1168344310346\">Factor: \\(2x+{x}^{2}-48\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344345183\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343132786\">\\(\\begin{array}{cc} &amp; 2x+{x}^{2}-48\\\\ \\text{First we put the terms in decreasing degree order.}&amp; {x}^{2}+2x-48\\\\ \\text{Factors will be two binomials with first terms x.}&amp; \\left(x\\right)\\left(x\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168342965887\">As shown in the table, you can use \\(-6,8\\) as the last terms of the binomials.<\/p>\n\n<div id=\"fs-id1168744045521\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\left(x-6\\right)\\left(x+8\\right)\\)<\/div>\n<table id=\"fs-id1168343060786\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u221248 and the second column is labeled sum of factors. In the first row are the factors negative1, 48 and the sum negative 1 + 48 = 47. The second row has the factors negative 2, 24 and the sum negative 2 plus 24 equals 22. The third row has the factors negative 2, 16 and the sum negative 3 + 16 = 13. The fourth row has the factors negative 4 + 12 and the sum negative 4 + 12 = 8. The fifth row has the factors negative 6, 8 and the sum negative 6 + 8 = 2.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(-48\\)<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-1,48\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-1+48=47\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">\\(-2,24\\)\n\\(-3,16\\)\n\\(-4,12\\)\n\\(-6,8\\)<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-2+24=22\\)\n\\(-3+16=13\\)\n\\(-4+12=8\\)\n\\(\\-6+8=2\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344628567\">Check.<\/p>\n<p id=\"fs-id1168344628570\">\\(\\left(x-6\\right)\\left(x+8\\right)\\)<\/p>\n<p id=\"fs-id1168344073620\">\\({x}^{2}-6q+8q-48\\)<\/p>\n<p id=\"fs-id1168344503873\">\\({x}^{2}+2x-48\\checkmark\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344533668\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344215917\" data-type=\"exercise\">\n<div id=\"fs-id1168344215919\" data-type=\"problem\">\n<p id=\"fs-id1168344215921\">Factor: \\(9m+{m}^{2}+18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344608367\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344608369\">\\(\\left(m+3\\right)\\left(m+6\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343095244\" data-type=\"problem\">\n<p id=\"fs-id1168343095246\">Factor: \\(-7n+12+{n}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343064270\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344110034\">\\(\\left(n-3\\right)\\left(n-4\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344197665\">Let\u2019s summarize the method we just developed to factor trinomials of the form \\({x}^{2}+bx+c\\).<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO:<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n\nFactor trinomials\u00a0 of the form \\({x}^{2}+bx+c\\).\n\nWhen we factor a trinomial, we look at the signs of its terms first to determine the signs of the binomial factors.\n<div id=\"fs-id1168344554934\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}\\hfill {x}^{2}+bx+c\\hfill \\\\ \\hfill \\left(x+m\\right)\\left(x+n\\right)\\hfill \\end{array}\\)<\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<p id=\"fs-id1168343070736\"><strong data-effect=\"bold\">When <em data-effect=\"italics\">c<\/em> is positive, <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have the same sign.<\/strong><\/p>\n\n<div id=\"fs-id1166503604137\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cc}\\text{b positive} &amp;\u00a0 \\text{b negative}\\\\ \\text{m, n positive} &amp;\\text{m, n negative}\\\\ {x}^{2}+5x+6 &amp; {x}^{2}-6x+8\\\\\u00a0 \\left(x+2\\right)\\left(x+3\\right) \\qquad &amp; \\qquad \\left(x-4\\right)\\left(x-2\\right) \\\\ \\text{same signs} &amp; \\text{same signs}\\end{array}\\)<\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<p id=\"fs-id1168343187597\"><strong data-effect=\"bold\">When <em data-effect=\"italics\">c<\/em> is negative, <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have opposite signs.<\/strong><\/p>\n\n<div id=\"fs-id1166503073425\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cc}{x}^{2}+x-12 &amp; {x}^{2}-2x-15\\\\ \\left(x+4\\right)\\left(x-3\\right) &amp; \\left(x-5\\right)\\left(x+3\\right)\\\\ \\text{opposite signs} &amp; \\text{opposite signs}\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1168344440295\">Notice that, in the case when <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have opposite signs, the sign of the one with the larger absolute value matches the sign of <em data-effect=\"italics\">b<\/em>.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bxy<\/em> + <em data-effect=\"italics\">cy<\/em><sup>2<\/sup><\/h1>\n<p id=\"fs-id1168343141621\">Sometimes you\u2019ll need to factor trinomials of the form \\({x}^{2}+bxy+c{y}^{2}\\) with two variables, such as \\({x}^{2}+12xy+36{y}^{2}\\). The first term, \\({x}^{2}\\), is the product of the first terms of the binomial factors, \\(x\\cdot x\\). The \\({y}^{2}\\) in the last term means that the second terms of the binomial factors must each contain <em data-effect=\"italics\">y<\/em>. To get the coefficients <em data-effect=\"italics\">b<\/em> and <em data-effect=\"italics\">c<\/em>, you use the same process summarized in the previous objective.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343008734\" data-type=\"problem\">\n<p id=\"fs-id1168343008736\">Factor: \\({x}^{2}+12xy+36{y}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343174999\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343175004\">\\(\\begin{array}{cc}&amp; {x}^{2}+12xy+36{y}^{2}\\\\ \\begin{array}{c}\\text{Note that the first terms are x. last terms}\\hfill \\\\ \\text{containy.}\\end{array} &amp; \\left(x_y\\right)\\left(x_y\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168344503372\">Find the numbers that multiply to 36 and add to 12<\/p>\n\n<table id=\"fs-id1168344603366\" class=\"grid\" summary=\"This table has two columns. The first column is labeled factors of 36 and the second column is labeled sum of factors. The first row has the two factors 1, 36 and the sum 1 + 36 = 37. The second row has the factors 2, 18 and the sum 2 + 18 = 20. The third row has the factors 3, 12 and the sum 3 + 12 = 15. The fourth row has the factors 4, 9 and the sum 4 + 9 = 13. The fifth row has the factors 6, 6 and the sum 6 + 6 = 12. This row has an asterisk.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of \\(36\\)<\/th>\n<th data-valign=\"top\" data-align=\"left\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1, 36<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(1+36=37\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2, 18<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(2+18=20\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3, 12<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(3+12=15\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">4, 9<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(4+9=13\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">6, 6<\/td>\n<td data-align=\"center\" data-valign=\"top\">\\(6+6=12\\text{*}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343000756\">Use 6 and 6 as the coefficients of the last terms.\u00a0 \u00a0\\(\\left(x+6y\\right)\\left(x+6y\\right)\\)<\/p>\nCheck your answer.\n\n\\(\\begin{array}{c}\\left(x+6y\\right)\\left(x+6y\\right) \\\\ {x}^{2}+6xy+6xy+36{y}^{2} \\\\ {x}^{2}+12xy+36{y}^{2}\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343128752\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343128756\" data-type=\"exercise\">\n<div id=\"fs-id1168343175338\" data-type=\"problem\">\n<p id=\"fs-id1168343175340\">Factor: \\({u}^{2}+11uv+28{v}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343062962\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343062964\">\\(\\left(u+4v\\right)\\left(u+7v\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343194963\" data-type=\"problem\">\n<p id=\"fs-id1168343194965\">Factor: \\({x}^{2}+13xy+42{y}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343004771\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343004773\">\\(\\left(x+6y\\right)\\left(x+7y\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344555684\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344555688\" data-type=\"exercise\">\n<div id=\"fs-id1168343004771\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343132295\" data-type=\"problem\">\n<p id=\"fs-id1168343132297\">Factor: \\({r}^{2}-8rx-9{s}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168342964500\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168342964505\">We need \\(r\\) in the first term of each binomial and \\(s\\) in the second term. The last term of the trinomial is negative, so the factors must have opposite signs.<\/p>\n<p id=\"fs-id1168344505665\">\\(\\begin{array}{cc} &amp; {r}^{2}-8rx-9{s}^{2}\\\\ \\text{Note that the first terms are r, last terms contain s.} &amp; \\left(r_s\\right)\\left(r_s\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168343130225\">Find the numbers that multiply to \\(-9\\) and add to \\(-8\\).<\/p>\n\n<table id=\"fs-id1168344603447\" class=\"grid\" style=\"height: 58px;\" summary=\"This table has two columns. The first column is labeled factors of \u22129 and the second column is labeled sum of factors. The first row has the factors 1, negative 9 and the sum 1 + (negative 9) = negative 8. This row has an asterisk. The second row has the factors negative 1, 9 and the sum negative 1 + 9 = 8. The third row has the factors 3, negative 3 and the sum 3 + (negative 3) = 0.\" data-label=\"\">\n<thead>\n<tr style=\"height: 13px;\" valign=\"top\">\n<th style=\"height: 13px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\">Factors of \\(-9\\)<\/th>\n<th style=\"height: 13px; width: 359.119px;\" data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\">\\(1,-9\\)<\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\">\\(1+\\left(-9\\right)=-8\\text{*}\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\">\\(-1,9\\)<\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\">\\(-1+9=8\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\">\\(3,-3\\)<\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\">\\(3+\\left(-3\\right)=0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344620205\">Check your answer.Use 1, -9 as coefficients of the last terms. \\(\\left(r+s\\right)\\left(r-9s\\right)\\)<\/p>\n\\(\\begin{array}{c}\\left(r-9s\\right)\\left(r+s\\right) \\\\{r}^{2}+rs-9rs-9{s}^{2} \\\\{r}^{2}-8rs-9{s}^{2}\\checkmark \\end{array}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344296891\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343023332\" data-type=\"exercise\">\n<div id=\"fs-id1168343023334\" data-type=\"problem\">\n<p id=\"fs-id1168343023336\">Factor: \\({a}^{2}-11ab+10{b}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343069911\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343069913\">\\(\\left(a-b\\right)\\left(a-10b\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344477412\" data-type=\"problem\">\n<p id=\"fs-id1168344477414\">Factor: \\({m}^{2}-13mn+12{n}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343035769\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168343035771\">\\(\\left(m-n\\right)\\left(m-12n\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343054681\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343054684\" data-type=\"exercise\">\n<div id=\"fs-id1168343035769\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344312555\" data-type=\"problem\">\n<p id=\"fs-id1168344312557\">Factor: \\({u}^{2}-9uv-12{v}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343246623\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344600930\">We need <em data-effect=\"italics\">u<\/em> in the first term of each binomial and \\(v\\) in the second term. The last term of the trinomial is negative, so the factors must have opposite signs.<\/p>\n<p id=\"fs-id1168344440611\">\\(\\begin{array}{cc} &amp; {u}^{2}-9uv-12{v}^{2}\\\\ \\text{Note that the first terms are u, last terms contain v.} &amp; \\left(u_v\\right)\\left(u_v\\right)\\end{array}\\)<\/p>\n<p id=\"fs-id1168343138131\">Find the numbers that multiply to \\(-12\\) and add to \\(-9\\).<\/p>\n\n<table id=\"fs-id1168344579863\" class=\"grid\" style=\"height: 105px;\" summary=\"This table has two columns. The first column is labeled factors of negative12 and the second column is labeled sum of factors. The first row has the factors 1, negative 12 and the sum 1 + negative 12 = negative 11. The second row has the factors negative 1, 12 and the sum negative 1 + 12 = 11. The third row has the factors 2, negative 6 and the sum 2 + (negative 6) = negative 4. The fourth row has the factors negative 2, 6 and the sum negative 2 + 6 = 4. The fifth row has the factors 3, negative 4 and the sum 3 + (negative 4) = negative 1. The sixth row has the factors negative 3, 4 and the sum negative 3 + 4 = 1.\" data-label=\"\">\n<thead>\n<tr style=\"height: 15px;\" valign=\"top\">\n<th style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">Factors of \\(-12\\)<\/th>\n<th style=\"width: 320.028px; height: 15px;\" data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(1,-12\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(1+\\left(-12\\right)=-11\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(1,12\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(-1+12=11\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(2,-6\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(2+\\left(-6\\right)=-4\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(-2,6\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(-2+6=4\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(3,-4\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(3+\\left(-4\\right)=-1\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(-3,4\\)<\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\">\\(-3+4=1\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343069930\">Note there are no factor pairs that give us \\(-9\\) as a sum. The trinomial is prime.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343119792\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344599076\" data-type=\"exercise\">\n<div id=\"fs-id1168344599078\" data-type=\"problem\">\n<p id=\"fs-id1168344599080\">Factor: \\({x}^{2}-7xy-10{y}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168344437739\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168344437741\">prime<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343128972\" data-type=\"problem\">\n<p id=\"fs-id1168343128974\">Factor: \\({p}^{2}+15pq+20{q}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168343054336\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168342979739\">prime<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1168344316915\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Factor trinomials of the form \\({x}^{2}+bx+c\\)<\/strong>\n<ol id=\"fs-id1168746486111\" class=\"stepwise\" type=\"1\">\n \t<li>Write the factors as two binomials with first terms <em data-effect=\"italics\">x<\/em>: \\(\\left(x\\right)\\left(x\\right)\\).<\/li>\n \t<li>Find two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> that\nMultiply to <em data-effect=\"italics\">c<\/em>, \\(m\\cdot n=c\\)\nAdd to <em data-effect=\"italics\">b<\/em>, \\(m+n=b\\)<\/li>\n \t<li>Use <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> as the last terms of the factors: \\(\\left(x+m\\right)\\left(x+n\\right)\\).<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Factor Trinomials of the Form \\({x}^{2}+bx+c\\)<\/h2>\n<p id=\"fs-id1168744119122\">In the following exercises, factor each trinomial of the form \\({x}^{2}+bx+c\\).<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. \\({x}^{2}+4x+3\\)<\/td>\n<td style=\"width: 50%;\">2. \\({y}^{2}+8y+7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. \\({m}^{2}+12m+11\\)<\/td>\n<td style=\"width: 50%;\">4. \\({b}^{2}+14b+13\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. \\({a}^{2}+9a+20\\)<\/td>\n<td style=\"width: 50%;\">6. \\({m}^{2}+7m+12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. \\({p}^{2}+11p+30\\)<\/td>\n<td style=\"width: 50%;\">8. \\({w}^{2}+10x+21\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. \\({n}^{2}+19n+48\\)<\/td>\n<td style=\"width: 50%;\">10. \\({b}^{2}+14b+48\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. \\({a}^{2}+25a+100\\)<\/td>\n<td style=\"width: 50%;\">12. \\({u}^{2}+101u+100\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. \\({x}^{2}-8x+12\\)<\/td>\n<td style=\"width: 50%;\">14. \\({q}^{2}-13q+36\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. \\({y}^{2}-18x+45\\)<\/td>\n<td style=\"width: 50%;\">16. \\({m}^{2}-13m+30\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. \\({x}^{2}-8x+7\\)<\/td>\n<td style=\"width: 50%;\">18. \\({y}^{2}-5y+6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\({p}^{2}+5p-6\\)<\/td>\n<td style=\"width: 50%;\">20. \\({n}^{2}+6n-7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. \\({y}^{2}-6y-7\\)<\/td>\n<td style=\"width: 50%;\">22. \\({v}^{2}-2v-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. \\({x}^{2}-x-12\\)<\/td>\n<td style=\"width: 50%;\">24. \\({r}^{2}-2r-8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. \\({a}^{2}-3a-28\\)<\/td>\n<td style=\"width: 50%;\">26. \\({b}^{2}-13b-30\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. \\({w}^{2}-5w-36\\)<\/td>\n<td style=\"width: 50%;\">28. \\({t}^{2}-3t-54\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. \\({x}^{2}+x+5\\)<\/td>\n<td style=\"width: 50%;\">30. \\({x}^{2}-3x-9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. \\(8-6x+{x}^{2}\\)<\/td>\n<td style=\"width: 50%;\">32. \\(7x+{x}^{2}+6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. \\({x}^{2}-12-11x\\)<\/td>\n<td style=\"width: 50%;\">34. \\(-11-10x+{x}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1168343007291\" data-type=\"exercise\">\n<div id=\"fs-id1168343007293\" data-type=\"problem\">\n<h2>Factor Trinomials of the Form \\({x}^{2}+bxy+c{y}^{2}\\)<\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168744271961\">In the following exercises, factor each trinomial of the form \\({x}^{2}+bxy+c{y}^{2}\\).<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. \\({p}^{2}+3pq+2{q}^{2}\\)<\/td>\n<td style=\"width: 50%;\">36. \\({m}^{2}+6mn+5{n}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. \\({r}^{2}+15rs+36{s}^{2}\\)<\/td>\n<td style=\"width: 50%;\">38. \\({u}^{2}+10uv+24{v}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. \\({m}^{2}-12mn+20{n}^{2}\\)<\/td>\n<td style=\"width: 50%;\">40. \\({p}^{2}-16pq+63{q}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. \\({x}^{2}-2xy-80{y}^{2}\\)<\/td>\n<td style=\"width: 50%;\">42. \\({p}^{2}-8pq-65{q}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. \\({m}^{2}-64mn-65{n}^{2}\\)<\/td>\n<td style=\"width: 50%;\">44. \\({p}^{2}-2pq-35{q}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. \\({a}^{2}+5ab-24{b}^{2}\\)<\/td>\n<td style=\"width: 50%;\">46. \\({r}^{2}+3rs-28{s}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. \\({x}^{2}-3xy-14{y}^{2}\\)<\/td>\n<td style=\"width: 50%;\">48. \\({u}^{2}-8uv-24{v}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. \\({m}^{2}-5mn+30{n}^{2}\\)<\/td>\n<td style=\"width: 50%;\">50. \\({c}^{2}-7cd+18{d}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1168343045418\" data-type=\"exercise\">\n<h2 id=\"fs-id1168343045420\" data-type=\"problem\">Mixed Practice<\/h2>\n<\/div>\n<p id=\"fs-id1168743433329\">In the following exercises, factor each expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. \\({u}^{2}-12u+36\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">52. \\({w}^{2}+4w-32\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. \\({x}^{2}-14x-32\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">54. \\({y}^{2}+41y+40\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. \\({r}^{2}-20rs+64{s}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">56. \\({x}^{2}-16xy+64{y}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. \\({k}^{2}+34k+120\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">58. \\({m}^{2}+29m+120\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. \\({y}^{2}+10y+15\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">60. \\({z}^{2}-3z+28\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. \\({m}^{2}+mn-56{n}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">62. \\({q}^{2}-29qr-96{r}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. \\({u}^{2}-17uv+30{v}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">64. \\({m}^{2}-31mn+30{n}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. \\({c}^{2}-8cd+26{d}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">66. \\({r}^{2}+11rs+36{s}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">67.<strong data-effect=\"bold\"> Consecutive integers<\/strong> Deirdre is thinking of two consecutive integers whose product is 56. The trinomial \\({x}^{2}+x-56\\) describes how these numbers are related. Factor the trinomial.<\/td>\n<td style=\"width: 50%;\">68.<strong data-effect=\"bold\"> Consecutive integers<\/strong> Deshawn is thinking of two consecutive integers whose product is 182. The trinomial \\({x}^{2}+x-182\\) describes how these numbers are related. Factor the trinomial.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">69. Many trinomials of the form \\({x}^{2}+bx+c\\) factor into the product of two binomials \\(\\left(x+m\\right)\\left(x+n\\right)\\). Explain how you find the values of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em>.<\/td>\n<td style=\"width: 50%;\">70. How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form \\({x}^{2}+bx+c\\) where \\(b\\) and \\(c\\) may be positive or negative numbers?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. Will factored \\({x}^{2}-x-20\\) as \\(\\left(x+5\\right)\\left(x-4\\right)\\). Bill factored it as \\(\\left(x+4\\right)\\left(x-5\\right)\\). Phil factored it as \\(\\left(x-5\\right)\\left(x-4\\right)\\). Who is correct? Explain why the other two are wrong.<\/td>\n<td style=\"width: 50%;\">72. Look at <a class=\"autogenerated-content\" href=\"#fs-id1168344083254\">(Figure)<\/a>, where we factored \\({y}^{2}+17y+60\\). We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">1.\u00a0\\(\\left(x+1\\right)\\left(x+3\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">3. \\(\\left(m+1\\right)\\left(m+11\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">5. \\(\\left(a+4\\right)\\left(a+5\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">7. \\(\\left(p+5\\right)\\left(p+6\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">9. \\(\\left(n+3\\right)\\left(n+16\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">11. \\(\\left(a+5\\right)\\left(a+20\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">13. \\(\\left(x-2\\right)\\left(x-6\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">15. \\(\\left(y-3\\right)\\left(y-15\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">17. \\(\\left(x-1\\right)\\left(x-7\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">19. \\(\\left(p-1\\right)\\left(p+6\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">21. \\(\\left(y+1\\right)\\left(y-7\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">23. \\(\\left(x-4\\right)\\left(x+3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">25. \\(\\left(a-7\\right)\\left(a+4\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">27. \\(\\left(w-9\\right)\\left(w+4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">29. prime<\/td>\n<td style=\"width: 50%; height: 16px;\">31. \\(\\left(x-4\\right)\\left(x-2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">33. \\(\\left(x-12\\right)\\left(x+1\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">35. \\(\\left(p+q\\right)\\left(p+2q\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">37. \\(\\left(r+3s\\right)\\left(r+12s\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">39. \\(\\left(m-2n\\right)\\left(m-10n\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. \\(\\left(x+8y\\right)\\left(x-10y\\right)\\)<\/td>\n<td style=\"width: 50%;\">43. \\(\\left(m+n\\right)\\left(m-65n\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. \\(\\left(a+8b\\right)\\left(a-3b\\right)\\)<\/td>\n<td style=\"width: 50%;\">47. prime<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. prime<\/td>\n<td style=\"width: 50%;\">51. \\(\\left(u-6\\right)\\left(u-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. \\(\\left(x+2\\right)\\left(x-16\\right)\\)<\/td>\n<td style=\"width: 50%;\">55. \\(\\left(r-4s\\right)\\left(r-16s\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">57. \\(\\left(k+4\\right)\\left(k+30\\right)\\)<\/td>\n<td style=\"width: 50%;\">59. prime<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61. \\(\\left(m+8n\\right)\\left(m-7n\\right)\\)<\/td>\n<td style=\"width: 50%;\">63. \\(\\left(u-15v\\right)\\left(u-2v\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. prime<\/td>\n<td style=\"width: 50%;\">67. \\(\\left(x+8\\right)\\left(x-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69. Answers may vary<\/td>\n<td style=\"width: 50%;\">71. Answers may vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cFactor Trinomials of the Form \\({x}^{2}+bx+c\\)\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/li>\n<li>Factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02db4b17730ec637e3f4c699969ade06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#121;&#43;&#99;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em> + <em data-effect=\"italics\">c<\/em><\/h1>\n<p id=\"fs-id1168344295319\">You have already learned how to multiply binomials using FOIL. Now you\u2019ll need to \u201cundo\u201d this multiplication\u2014to start with the product and end up with the factors. Let\u2019s look at an example of multiplying binomials to refresh your memory.<\/p>\n<p><span id=\"fs-id1168344504686\" data-type=\"media\" data-alt=\"This figure shows the steps of multiplying the factors (x + 2) times (x + 3). The multiplying is completed using FOIL to demonstrate. The first term is x squared and is below F. The second term is 3 x below \u201cO\u201d. The third term is 2 x below \u201cI\u201d. The fourth term is 6 below L. The simplified product is then given as x 2 plus 5 x + 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_Elem20Alg_Figure_07_02_001_img_new.jpg\" alt=\"This figure shows the steps of multiplying the factors (x + 2) times (x + 3). The multiplying is completed using FOIL to demonstrate. The first term is x squared and is below F. The second term is 3 x below \u201cO\u201d. The third term is 2 x below \u201cI\u201d. The fourth term is 6 below L. The simplified product is then given as x 2 plus 5 x + 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1168343053818\">To factor the trinomial means to start with the product, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-796dbf4877c44d45b95e2f7845612068_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/>, and end with the factors, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baf4fe8c0d80c8752b56a98c9a0ad94b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/>. You need to think about where each of the terms in the trinomial came from.<\/p>\n<p id=\"fs-id1168343004832\">The <em data-effect=\"italics\">first term<\/em> came from multiplying the first term in each binomial. So to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> in the product, each binomial must start with an <em data-effect=\"italics\">x<\/em>.<\/p>\n<div id=\"fs-id1168344112344\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1160e324b369044be5fc4c69d791144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"89\" style=\"vertical-align: -16px;\" \/><\/div>\n<p id=\"fs-id1168344149571\">The <em data-effect=\"italics\">last term<\/em> in the trinomial came from multiplying the last term in each binomial. So the last terms must multiply to 6<\/p>\n<p id=\"fs-id1168344335725\">What two numbers multiply to 6?<\/p>\n<p id=\"fs-id1168343239771\">The factors of 6 could be 1 and 6, or 2 and 3. How do you know which pair to use?<\/p>\n<p id=\"fs-id1168344516045\">Consider the <em data-effect=\"italics\">middle term<\/em>. It came from adding the outer and inner terms.<\/p>\n<p id=\"fs-id1168343129934\">So the numbers that must have a product of 6 will need a sum of 5. We\u2019ll test both possibilities and summarize the results in the table below\u2014the table will be very helpful when you work with numbers that can be factored in many different ways.<\/p>\n<table id=\"fs-id1168344555789\" class=\"grid\" summary=\"This table consists of two columns and 3 rows. The first row of the first column reads \u201cFactors od 6.\u201d The next row down includes the factors 1, 6. The third row includes the factors 2, 3. The second column head reads \u201csum of factors.\u201d The next row under this reads 1 plus 6 equals 7. The next row down reads 2 plus 3 equals 5.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df753e623ad26ec2f5eb5a687b10bcef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2160129354abfb9d30f319aed1a227bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#54;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f3f8e3978872d71d76b443c082b9ebd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#44;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32ba1ddb986c9d1c32cef187fa6bd321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#51;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344368014\">We see that 2 and 3 are the numbers that multiply to 6 and add to 5. So we have the factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-796dbf4877c44d45b95e2f7845612068_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/>. They are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baf4fe8c0d80c8752b56a98c9a0ad94b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id1168344111440\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17a390815faf953f4f7f46bf5144e303_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#114;&#111;&#100;&#117;&#99;&#116;&#125;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"241\" style=\"vertical-align: -16px;\" \/><\/div>\n<p id=\"fs-id1168344120416\">You should check this by multiplying.<\/p>\n<p id=\"fs-id1168344332394\">Looking back, we started with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-796dbf4877c44d45b95e2f7845612068_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/>, which is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b41cd8020624a683feb6c7e88b71c9ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49cf0d6e306c1aff3581f57553ef715d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>. We factored it into two binomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ae1e411e03346a32e77563c00d91b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-980ac67ad78a228834b3ce882d00a53f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<div id=\"fs-id1168344306410\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-824fced1160d9682991c45dcba6fcfe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"300\" style=\"vertical-align: -16px;\" \/><\/div>\n<p id=\"fs-id1168344104178\">To get the correct factors, we found two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> whose product is <em data-effect=\"italics\">c<\/em> and sum is <em data-effect=\"italics\">b<\/em>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Factor Trinomials of the Form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id1168343096854\" data-type=\"exercise\">\n<div id=\"fs-id1168344202406\" data-type=\"problem\">\n<p id=\"fs-id1168343007559\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9fa2dc6db24b714c288aebd1537bf222_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343188796\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1168343052084\" data-type=\"media\" data-alt=\"This table gives the steps for factoring x squared + 7 x + 12. The first row states the first step \u201cwrite the factors as two binomials with first terms x\u201d. In the second column of the first row it states, \u201cwrite two sets of parentheses and put x as the first term\u201d. In the third column, it has the expression x squared + 7 x +12. Below the expression are two sets of parentheses with x as the first term.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002a_img_new.jpg\" alt=\"This table gives the steps for factoring x squared + 7 x + 12. The first row states the first step \u201cwrite the factors as two binomials with first terms x\u201d. In the second column of the first row it states, \u201cwrite two sets of parentheses and put x as the first term\u201d. In the third column, it has the expression x squared + 7 x +12. Below the expression are two sets of parentheses with x as the first term.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344116515\" data-type=\"media\" data-alt=\"The second row states the second step \u201cfind two numbers m and n that multiply to c, m times n = c and add to b, m + n = b\u201d. In the second column of the second row are the factors of 12 and their sums. 1,12 with sum 1 + 12 = 13. 2, 6 with sum 2 + 6 =8. 3, 4 with sum 3 + 4 = 7.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002b_img_new.jpg\" alt=\"The second row states the second step \u201cfind two numbers m and n that multiply to c, m times n = c and add to b, m + n = b\u201d. In the second column of the second row are the factors of 12 and their sums. 1,12 with sum 1 + 12 = 13. 2, 6 with sum 2 + 6 =8. 3, 4 with sum 3 + 4 = 7.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344084942\" data-type=\"media\" data-alt=\"The third row states \u201cuse m and n as the last terms of the factors\u201d. The second column states \u201cuse 3 and 4 as the last terms of the binomials\u201d. The third column in this row has the product (x + 3)(x + 4).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002c_img_new.jpg\" alt=\"The third row states \u201cuse m and n as the last terms of the factors\u201d. The second column states \u201cuse 3 and 4 as the last terms of the binomials\u201d. The third column in this row has the product (x + 3)(x + 4).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344441086\" data-type=\"media\" data-alt=\"In the fourth row the statement is \u201ccheck by multiplying the factors\u201d. The product of (x + 3)(x +4) is shown to be x 2 + 7 x + 12.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_02_002d_img_new.jpg\" alt=\"In the fourth row the statement is \u201ccheck by multiplying the factors\u201d. The product of (x + 3)(x +4) is shown to be x 2 + 7 x + 12.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344080907\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344075573\" data-type=\"exercise\">\n<div id=\"fs-id1168344228715\" data-type=\"problem\">\n<p id=\"fs-id1168343160986\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d43d27073cae4a5a5910e00a7935afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344075926\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344318972\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7b04144808fbdaa1de93f5d9fdda3ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344316847\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344343972\" data-type=\"exercise\">\n<div id=\"fs-id1168344285818\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1168344249495\" data-type=\"solution\">\n<p id=\"fs-id1168344370815\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344285818\" data-type=\"problem\">\n<p id=\"fs-id1168343113310\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff0fc5310dec42bb0bb8a9c85f2f36c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344249495\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344370815\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-03dd23a2d0bf848be0eaae904a89cfb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344254623\">Let\u2019s summarize the steps we used to find the factors.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO:<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<p>Factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<ol id=\"fs-id1168744022333\" class=\"stepwise\" type=\"1\">\n<li>Write the factors as two binomials with first terms <em data-effect=\"italics\">x<\/em>: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e7ec1c80f4c0ef9b6ffd15a6a01941e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#41;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\" \/>.<\/li>\n<li>Find two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> that<br \/>\nMultiply to <em data-effect=\"italics\">c<\/em>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fbd6bb5b853a59432595a4e23342cfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#61;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"71\" style=\"vertical-align: 0px;\" \/><br \/>\nAdd to <em data-effect=\"italics\">b<\/em>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3016e48f6b3e5e5184cd3010a2b9d479_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#43;&#110;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: -2px;\" \/><\/li>\n<li>Use <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> as the last terms of the factors: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-612a2d96dc1eee1dfd8d2384d5741ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344193768\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343140469\" data-type=\"problem\">\n<p id=\"fs-id1168343174220\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5c6e66c9998dbdf1e73bf94d83ba2b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#117;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344074028\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343062758\">Notice that the variable is <em data-effect=\"italics\">u<\/em>, so the factors will have first terms <em data-effect=\"italics\">u<\/em>.<\/p>\n<p id=\"fs-id1168344330736\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6210ba934445c5fab90c0bea7c7ea4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#38;&#32;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#117;&#43;&#50;&#52;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#97;&#115;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#117;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"537\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1168344320345\">Find two numbers that: multiply to 24 and add to 11<\/p>\n<table id=\"fs-id1168343095225\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 24 and the second column is labeled sum of the factors. The first row is 1, 24 with sum in the second column 1 + 24 = 25. The second row is 2, 12 with sum 2 + 12 = 14. The third row is 3,8 with sum 3 + 8 = 11. The fourth row is 4,6 with sum 4 + 6 = 10.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"middle\" data-align=\"center\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/><\/th>\n<th data-valign=\"middle\" data-align=\"center\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad8c7e8b6c6c08b2427fbca101db2f3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc4c73db9d1fa786904875312bbe5b97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#50;&#52;&#61;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eaf00c48a26f16fb455df9642781e6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#44;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-046801248edff89859e3647053217d95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#49;&#50;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3dccc74cc22e35bcc997cb98a0103c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ee929b471530b946e59ba9bed14176f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#56;&#61;&#49;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f8d2415ee2ced4d178603e3092d30b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#44;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca5db36de69f5bcc397a7a8af3dfd44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"81\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344218997\">Use 3 and 8 as the last terms of the binomials.\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6be4f92d94b47ac516aaf4e8bf7188bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>Check.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb46232428772ba9f39cc6e3f0657ab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#117;&#43;&#56;&#117;&#43;&#50;&#52;&#32;&#92;&#92;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#117;&#43;&#50;&#52;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"139\" style=\"vertical-align: -24px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-415098b3d418dbe9761f74aca67c3df0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#113;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id1168344327546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343004687\" data-type=\"exercise\">\n<div id=\"fs-id1168343054538\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343130483\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17cddfa10970b6bde868ec6f0cb4e68d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343097190\" data-type=\"problem\">\n<p id=\"fs-id1168343097192\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf4b29e99e04631fcc50c7841657c302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#116;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344303612\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344254324\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d011056a166f607a906713a2d7fb26bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344327546\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343004687\" data-type=\"exercise\">\n<div id=\"fs-id1168343004689\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344602096\" data-type=\"problem\">\n<p id=\"fs-id1168344602098\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75007ce6e065b4b2cb46d40dfcb2bc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#43;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344309961\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343060258\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ea97d0ff25d1ceb91012f64faad7890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#38;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#43;&#54;&#48;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#97;&#115;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#121;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"534\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1168343187961\">Find two numbers that multiply to 60 and add to 17<\/p>\n<table id=\"fs-id1168344371538\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 60 and the second column is labeled sum of factors. The first row has 1, 60 with sum 1 + 60 = 61. The second row has 2, 30 with sum 2 + 30 = 32. The third row has 3, 20 with sum 3 + 20 = 23. The fourth row has 4, 15 with sum 4 + 15 = 19. The fifth row has 5, 12 with sum 5 + 12 = 17 (this has an asterisk). The last row has 6,10 with sum 6 + 10 = 16.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7029ea134aa43ac5ffd9f780e196307d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49150b8c9a7e5c63332f22776f09b248_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75725094e7b9049bf46f76f9c6bd32ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#54;&#48;&#61;&#54;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b677dcb3340d199e62b28aa4c5a52fb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#44;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9abd9dfd84772c4837b53de2608197c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#51;&#48;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07f9df23a462297f65584ad4456da91e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a85ce76e1c37583692772d2c5bc5a38f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#50;&#48;&#61;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b35c13e7848b0f71608c69b740d4ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#44;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f38bfd1498ca8a946d6617767ae0af3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#49;&#53;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17682f4a610f27d0d9597feab925b871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#44;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1262d68ce6da369525d8e841e6f980b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#49;&#50;&#61;&#49;&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b760fff9f77175a16d527db92309c62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#44;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9af3df850063f3d3d73bea0094d29623_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#49;&#48;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344593946\">Use 5 and 12 as the last terms.\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57d285a00f7def4f4fa2b44d67d2bd5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>Check.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ded2538174d5cd99188e3c87fe18ea7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#40;&#121;&#43;&#53;&#41;&#40;&#121;&#43;&#49;&#50;&#41;&#32;&#92;&#92;&#32;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#121;&#43;&#53;&#121;&#43;&#54;&#48;&#41;&#32;&#92;&#92;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#43;&#54;&#48;&#41;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"157\" style=\"vertical-align: -27px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343070207\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344315968\" data-type=\"exercise\">\n<div id=\"fs-id1168344303612\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344108342\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344438118\" data-type=\"exercise\">\n<div id=\"fs-id1168344438120\" data-type=\"problem\">\n<p id=\"fs-id1168344438122\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1d786426d39ed3da63b40dbac3c4ca3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#57;&#120;&#43;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343244794\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343244796\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5db846a5140f9efffd160d90be9e594_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343046948\" data-type=\"problem\">\n<p id=\"fs-id1168343070859\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3efc44dba3d7f204b77f415527d6fa97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#51;&#118;&#43;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344592817\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344592819\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2c65772efa4c46128a6617fc2cbadcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#43;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em>\u00a0+ <em data-effect=\"italics\">c <\/em>with <em data-effect=\"italics\">b<\/em> Negative, <em data-effect=\"italics\">c<\/em> Positive<\/h1>\n<p id=\"fs-id1168344299853\">In the examples so far, all terms in the trinomial were positive. What happens when there are negative terms? Well, it depends which term is negative. Let\u2019s look first at trinomials with only the middle term negative.<\/p>\n<p id=\"fs-id1168344299856\">Remember: To get a negative sum and a positive product, the numbers must both be negative.<\/p>\n<p id=\"fs-id1168343096498\">Again, think about FOIL and where each term in the trinomial came from. Just as before,<\/p>\n<ul id=\"fs-id1168343096501\" data-bullet-style=\"bullet\">\n<li>the first term, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>, comes from the product of the two first terms in each binomial factor, <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>;<\/li>\n<li>the positive last term is the product of the two last terms<\/li>\n<li>the negative middle term is the sum of the outer and inner terms.<\/li>\n<\/ul>\n<p id=\"fs-id1168342965159\">How do you get a <em data-effect=\"italics\">positive product<\/em> and a <em data-effect=\"italics\">negative sum<\/em>? With two negative numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344108782\" data-type=\"problem\">\n<p id=\"fs-id1168343062436\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ee5d00dba2d690fd4248e9e2a8a027d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#116;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343239283\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344503443\">Again, with the positive last term, 28, and the negative middle term, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70e399486bf9f1eb789f4704a469d66a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"37\" style=\"vertical-align: -1px;\" \/>, we need two negative factors. Find two numbers that multiply 28 and add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1168344296828\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1f8b4980b7a63a618d0399adcf5bb5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#38;&#32;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#116;&#43;&#50;&#56;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#97;&#115;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"527\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1168343045607\">Find two numbers that: multiply to 28 and add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<table id=\"fs-id1168344106593\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 28 and the second column is labeled sum of factors. The first row has the factors negative 1, negative 28 and the sum negative 1 plus 9 minus 28) = negative 29. The second row has the factors negative 2, negative 14 and the sum negative 2 + (negative 14) = negative 16. The third row has the factors negative 4, negative 7 and the sum negative 4 + (negative 7) = negative 11. This one has an asterisk.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80588c2af70b499bde2614a130c98b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a57cb4c2609920411b5cd5cd732f33e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-593dd4428567ba94ef44b4b66369f65d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e341b90dee148791eb5b0d3bfa5cb269_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#44;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47ef5d130a8b1687052df85d435514a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ee3d86d47c03e58a526b9a615eb010b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#44;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa5935b567675ddee63c8e1f2dc8aa30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343060797\">Use -4, -7 as the last terms of the binomials.\u00a0 \u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f45bba5770970fa32f2d6e2199f56f75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>Check.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff6539b075af3d725adf3bc967633be7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#116;&#45;&#52;&#116;&#43;&#50;&#56;&#92;&#92;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#116;&#43;&#50;&#56;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"128\" style=\"vertical-align: -24px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343035188\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343035191\" data-type=\"exercise\">\n<div id=\"fs-id1168343190090\" data-type=\"problem\">\n<p id=\"fs-id1168343190092\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97e3e8f7f8c5e925504140a6724c1d0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#117;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344363425\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344363427\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53be6e377ffa29cef62526b5a51c1c23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343061523\" data-type=\"problem\">\n<p id=\"fs-id1168343061525\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9376b3bdd64e4533997f25ecc2268881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#121;&#43;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343072480\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343072482\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60b9067b1e73ee9109767625d9669cf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bx<\/em>\u00a0+ <em data-effect=\"italics\">c <\/em>with <em data-effect=\"italics\">c<\/em> Negative<\/h1>\n<p id=\"fs-id1168344394803\">Now, what if the last term in the trinomial is negative? Think about FOIL. The last term is the product of the last terms in the two binomials. A negative product results from multiplying two numbers with opposite signs. You have to be very careful to choose factors to make sure you get the correct sign for the middle term, too.<\/p>\n<p id=\"fs-id1168344357952\">Remember: To get a negative product, the numbers must have different signs.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344317637\" data-type=\"problem\">\n<p id=\"fs-id1168344317639\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d9bd90eeee57808591f1bb07cb144d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#122;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344074937\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343052674\">To get a negative last term, multiply one positive and one negative. We need factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> that add to positive 4<\/p>\n<table id=\"fs-id1168343062206\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of negative 5 and the second column is labeled sum of factors. The first row has the factors 1, negative 5 and the sum 1 + (negative 5) = negative 4. The second row has the factors negative 1, 5 and the sum negative 1 + 5 = 4.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6627b753967d6f5239d08969eea9f3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1eae7b74b455a87b3264d9d6d5bbf87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdfabb8d532e3f4159480790474ff49e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22c0d1c8e968af119b0ce4506e3ff1bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#53;&#61;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"93\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343008142\">Notice: We listed both <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6627b753967d6f5239d08969eea9f3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdfabb8d532e3f4159480790474ff49e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/> to make sure we got the sign of the middle term correct.<\/p>\n<p id=\"fs-id1168344336620\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e30ccde673bac63aa05ed383cef879e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#99;&#125;&#32;&#38;&#32;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#122;&#45;&#53;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#119;&#105;&#108;&#108;&#32;&#98;&#101;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#122;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#115;&#101;&#32;&#45;&#49;&#44;&#32;&#53;&#32;&#97;&#115;&#32;&#116;&#104;&#101;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"498\" style=\"vertical-align: -27px;\" \/><\/p>\n<p>Check.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b45499f2f9630e591c882e6748bc18ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#122;&#45;&#49;&#122;&#45;&#53;&#32;&#92;&#92;&#32;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#122;&#45;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"126\" style=\"vertical-align: -24px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344199736\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344199740\" data-type=\"exercise\">\n<div id=\"fs-id1168344299180\" data-type=\"problem\">\n<p id=\"fs-id1168344299182\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a1607617799f7b2c1dd3ec8e528944b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#104;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#104;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343244524\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343244526\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1bda97a963e6310939e917a756f4915c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#104;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#104;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343244830\" data-type=\"problem\">\n<p id=\"fs-id1168343244833\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97cb7a09a695b96a705e46b084633c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#43;&#107;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344440923\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344440925\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb66e0021e7dfd84c9b88d07a536c87d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344215499\">Let\u2019s make a minor change to the last trinomial and see what effect it has on the factors.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343247201\" data-type=\"problem\">\n<p id=\"fs-id1168344282144\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97018543e31bf937590eec56ff37f862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#122;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344314789\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343046964\">This time, we need factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> that add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<table id=\"fs-id1168343195050\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u22125 and the second column is labeled sum of factors. The first row has the factors 1, negative 5 and the sum 1 + (negative 5) = negative 4. This row has an asterisk. The second row has the factors negative 1, 5 and the sum negative 1 + 5 = 4.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6627b753967d6f5239d08969eea9f3eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d419148f094d7351ad4fa52dded80ea6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdfabb8d532e3f4159480790474ff49e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-561de43afa02f7c3850bbc5e68a7f12d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#53;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343003096\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-074c11761ec471455c3038be7489f4d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#99;&#125;&#38;&#32;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#122;&#45;&#53;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#119;&#105;&#108;&#108;&#32;&#98;&#101;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#122;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#115;&#101;&#32;&#49;&#44;&#32;&#45;&#53;&#32;&#97;&#115;&#32;&#116;&#104;&#101;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"498\" style=\"vertical-align: -27px;\" \/><\/p>\n<p>Check.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66cf8ead79481d64ccb5fd3062772047_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#122;&#43;&#49;&#122;&#45;&#53;&#32;&#92;&#92;&#32;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#122;&#45;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"126\" style=\"vertical-align: -23px;\" \/><\/p>\n<p id=\"fs-id1168343047355\">Notice that the factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97018543e31bf937590eec56ff37f862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#122;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -1px;\" \/> are very similar to the factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d9bd90eeee57808591f1bb07cb144d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#122;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -2px;\" \/>. It is very important to make sure you choose the factor pair that results in the correct sign of the middle term.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344517387\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343053892\" data-type=\"exercise\">\n<div id=\"fs-id1168343053894\" data-type=\"problem\">\n<p id=\"fs-id1168343053896\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58fe5e0aa625b83e532020c1eb859701_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343052867\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343158900\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ba0f486670d3a2eef840c28aaa6eb3d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344424372\" data-type=\"problem\">\n<p id=\"fs-id1168344424374\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ed326c12014877a12e6e2b4887b8149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#121;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344072690\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344072692\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-150a20fc1c8d9205302dde7495e642e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342967370\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344424370\" data-type=\"exercise\">\n<div id=\"fs-id1168344072690\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343007276\" data-type=\"problem\">\n<p id=\"fs-id1168343238382\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32f5c7308a1c34043431cc89483bfb6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#113;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343024975\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343174963\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e568c83fc4fa8e7cf33d4167ebb76687_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#38;&#32;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#113;&#45;&#49;&#53;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#119;&#105;&#108;&#108;&#32;&#98;&#101;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#113;&#46;&#125;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#111;&#117;&#32;&#99;&#97;&#110;&#32;&#117;&#115;&#101;&#32;&#51;&#44;&#32;&#45;&#53;&#32;&#97;&#115;&#32;&#116;&#104;&#101;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#46;&#125;&#38;&#32;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"498\" style=\"vertical-align: -34px;\" \/><\/p>\n<table id=\"fs-id1168344475602\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u221215 and the second column is labeled sum of factors. The first row has the factors 1, \u221215 and the sum 1 + (negative 15) = negative 14. The second row has the factors negative 1, 15 and the sum negative 1 + 15 = 14. The third row has the factors 3, negative 5 and the sum 3 + negative 5 = negative 2. This row has an asterisk. The fourth row has the factors negative 3, 5 and the sum negative 3 + 5 = 2.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0329d19b932005c996d83dbb9e09ffed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d4f25e33dff6d3a85d40053055a925a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae856a3adaaa4ee36e30d586264cffc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c78bd56aaf4bcae22190d80ec771a160_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fc9a95eeaa6ba20ebefb3825e3aeb53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#49;&#53;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-006243e2d0fa1a89a3e7c97cd3843d66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c37f68528f7f5faf62868784e71696a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-473f6590e4330acd7f3d846dfd4741fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#44;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f0d3976eca234ae402550ce3bc4b35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#43;&#53;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168342964041\">Check.<\/p>\n<p id=\"fs-id1168343188574\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d23c707592880faa65b799cca4bd2f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-id1168343063093\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2b3a7beaa8229442d5143c8733a6389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#113;&#43;&#51;&#113;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1168342965730\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c52657c432d820c28dde123b0f93ea54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#113;&#45;&#49;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47425fb197ecc9f14dc3fb7896ef9c50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1168343045190\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343045194\" data-type=\"exercise\">\n<div id=\"fs-id1168344076484\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343187780\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80d41acb692ed4eb040bec86e56c71d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342985416\" data-type=\"problem\">\n<p id=\"fs-id1168342985419\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a4464d74d273dafa844859747c31f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#115;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343187846\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344120004\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff47e5edc4458f3191c9583ca2c9c3c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168343175288\">Some trinomials are prime. The only way to be certain a trinomial is prime is to list all the possibilities and show that none of them work.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343053886\" data-type=\"problem\">\n<p id=\"fs-id1168343053889\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a9a90e91529c16aceff413619dbd688_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#121;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343188057\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343188063\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61bd6b1e67bb19ed3a142eff69ec364b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#38;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#121;&#43;&#49;&#53;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#119;&#105;&#108;&#108;&#32;&#98;&#101;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#101;&#114;&#109;&#115;&#32;&#121;&#46;&#125;&#32;&#38;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"416\" style=\"vertical-align: -26px;\" \/><\/p>\n<table id=\"fs-id1168344294638\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of 15 and the second column is labeled sum of factors. The first row has the factors negative 1, negative 15 and the sum negative 1 + (negative 15) = negative 16. The second row has the factors negative 3, negative 5 and the sum negative 3 + (negative 5) = negative 8.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of 15<\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4c981ec3bff16b9e06bf0cedbcec89a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb5aca183e64c7c4ca103c7096edc391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bf003eeb1e85358611a44141103632b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f413b0f7c3be2c988eb078a7a485a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344520795\">As shown in the table, none of the factors add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>; therefore, the expression is prime.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344315809\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344441069\" data-type=\"exercise\">\n<div id=\"fs-id1168344441071\" data-type=\"problem\">\n<p id=\"fs-id1168344441073\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ed25a9cb7fcf743e68717d38577688e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#109;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343054990\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344108517\">prime<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343048175\" data-type=\"problem\">\n<p id=\"fs-id1168343048177\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-050d25f76426ce7ef0564f407ce9f56c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#110;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168342981700\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168342981702\">prime<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344108524\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344108527\" data-type=\"exercise\">\n<div id=\"fs-id1168342981700\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344310344\" data-type=\"problem\">\n<p id=\"fs-id1168344310346\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a66b990438d964d417f135d6fd2e3f3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344345183\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343132786\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f762d3a6ba0994aa4e46c4349d7ef30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#38;&#32;&#50;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#56;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#105;&#114;&#115;&#116;&#32;&#119;&#101;&#32;&#112;&#117;&#116;&#32;&#116;&#104;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#105;&#110;&#32;&#100;&#101;&#99;&#114;&#101;&#97;&#115;&#105;&#110;&#103;&#32;&#100;&#101;&#103;&#114;&#101;&#101;&#32;&#111;&#114;&#100;&#101;&#114;&#46;&#125;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#52;&#56;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#119;&#105;&#108;&#108;&#32;&#98;&#101;&#32;&#116;&#119;&#111;&#32;&#98;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#115;&#32;&#119;&#105;&#116;&#104;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#120;&#46;&#125;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"503\" style=\"vertical-align: -27px;\" \/><\/p>\n<p id=\"fs-id1168342965887\">As shown in the table, you can use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0feadae254325e6173e0c16dafd0d2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#44;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/> as the last terms of the binomials.<\/p>\n<div id=\"fs-id1168744045521\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dc928c59945c71bc8fdbc68ca6da9a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/div>\n<table id=\"fs-id1168343060786\" class=\"unnumbered\" summary=\"This table has two columns. The first column is labeled factors of \u221248 and the second column is labeled sum of factors. In the first row are the factors negative1, 48 and the sum negative 1 + 48 = 47. The second row has the factors negative 2, 24 and the sum negative 2 plus 24 equals 22. The third row has the factors negative 2, 16 and the sum negative 3 + 16 = 13. The fourth row has the factors negative 4 + 12 and the sum negative 4 + 12 = 8. The fifth row has the factors negative 6, 8 and the sum negative 6 + 8 = 2.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-08ed8320699be2770837da731d65c7c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/th>\n<th data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bac41d333e4a6d567447dbd910611b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7ee95e2a099808de59dd9f2826b59b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#52;&#56;&#61;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43a37d68cc55d87d54bf5c7a057d9ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#44;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c06f323b87101b1292bc24ce6f4e8d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#44;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d742fba003c9601d8d4259d9ac676e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#44;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0feadae254325e6173e0c16dafd0d2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#44;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2bb50043af5215cee90183cea87327a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#50;&#52;&#61;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"102\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0cd5f0639c8774bc4e2e2418dae9f2d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#43;&#49;&#54;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"103\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2dfe13d23c080ea6b03a26a5b3aede9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#43;&#49;&#50;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"94\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b21bf186d58854c53c084c72ca33bc20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#45;&#54;&#43;&#56;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344628567\">Check.<\/p>\n<p id=\"fs-id1168344628570\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dc928c59945c71bc8fdbc68ca6da9a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-id1168344073620\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-183e6d6f03571442d8a3226e6888f409_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#113;&#43;&#56;&#113;&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1168344503873\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdb5076ebf9974b1643f232cbeaa2b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#52;&#56;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"112\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344533668\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344215917\" data-type=\"exercise\">\n<div id=\"fs-id1168344215919\" data-type=\"problem\">\n<p id=\"fs-id1168344215921\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f7b3398184f5aa14a8dd385e2a1a3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#109;&#43;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344608367\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344608369\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02a062d49bf775762aecec8657e8b7c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343095244\" data-type=\"problem\">\n<p id=\"fs-id1168343095246\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b23914b24fd4b88cdec5e8a43d97a16d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#110;&#43;&#49;&#50;&#43;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"111\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343064270\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344110034\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8141f2c9cc8a866409b13fe77def73e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344197665\">Let\u2019s summarize the method we just developed to factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO:<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<p>Factor trinomials\u00a0 of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p>When we factor a trinomial, we look at the signs of its terms first to determine the signs of the binomial factors.<\/p>\n<div id=\"fs-id1168344554934\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-88599bd21300cfc1ff0768d6984c6280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"119\" style=\"vertical-align: -15px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<p id=\"fs-id1168343070736\"><strong data-effect=\"bold\">When <em data-effect=\"italics\">c<\/em> is positive, <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have the same sign.<\/strong><\/p>\n<div id=\"fs-id1166503604137\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-89d581ae4f7a25b5f76e0b3f4e03d2f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#32;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#44;&#32;&#110;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#32;&#38;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#44;&#32;&#110;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#92;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;&#43;&#56;&#92;&#92;&#32;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#109;&#101;&#32;&#115;&#105;&#103;&#110;&#115;&#125;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#109;&#101;&#32;&#115;&#105;&#103;&#110;&#115;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"104\" width=\"309\" style=\"vertical-align: -48px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<p id=\"fs-id1168343187597\"><strong data-effect=\"bold\">When <em data-effect=\"italics\">c<\/em> is negative, <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have opposite signs.<\/strong><\/p>\n<div id=\"fs-id1166503073425\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d687eba7ed33058046811260af32c912_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#49;&#50;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#45;&#49;&#53;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#32;&#115;&#105;&#103;&#110;&#115;&#125;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#32;&#115;&#105;&#103;&#110;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"238\" style=\"vertical-align: -26px;\" \/><\/div>\n<p id=\"fs-id1168344440295\">Notice that, in the case when <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> have opposite signs, the sign of the one with the larger absolute value matches the sign of <em data-effect=\"italics\">b<\/em>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor Trinomials of the Form <em data-effect=\"italics\">x<\/em><sup>2<\/sup> + <em data-effect=\"italics\">bxy<\/em> + <em data-effect=\"italics\">cy<\/em><sup>2<\/sup><\/h1>\n<p id=\"fs-id1168343141621\">Sometimes you\u2019ll need to factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02db4b17730ec637e3f4c699969ade06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#121;&#43;&#99;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/> with two variables, such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d57d05f59999c480cd584b3d949ea7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#121;&#43;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -4px;\" \/>. The first term, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/>, is the product of the first terms of the binomial factors, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f78fc3cb11185d297486254db549b8fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"33\" style=\"vertical-align: 0px;\" \/>. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f72e617ab66ab04529ce474aaeeba224_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\" \/> in the last term means that the second terms of the binomial factors must each contain <em data-effect=\"italics\">y<\/em>. To get the coefficients <em data-effect=\"italics\">b<\/em> and <em data-effect=\"italics\">c<\/em>, you use the same process summarized in the previous objective.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343008734\" data-type=\"problem\">\n<p id=\"fs-id1168343008736\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d57d05f59999c480cd584b3d949ea7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#121;&#43;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343174999\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343175004\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d500f4d0962701f27c075fcb3ae0138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#121;&#43;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#111;&#116;&#101;&#32;&#116;&#104;&#97;&#116;&#32;&#116;&#104;&#101;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#97;&#114;&#101;&#32;&#120;&#46;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#116;&#97;&#105;&#110;&#121;&#46;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#95;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#95;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"483\" style=\"vertical-align: -26px;\" \/><\/p>\n<p id=\"fs-id1168344503372\">Find the numbers that multiply to 36 and add to 12<\/p>\n<table id=\"fs-id1168344603366\" class=\"grid\" summary=\"This table has two columns. The first column is labeled factors of 36 and the second column is labeled sum of factors. The first row has the two factors 1, 36 and the sum 1 + 36 = 37. The second row has the factors 2, 18 and the sum 2 + 18 = 20. The third row has the factors 3, 12 and the sum 3 + 12 = 15. The fourth row has the factors 4, 9 and the sum 4 + 9 = 13. The fifth row has the factors 6, 6 and the sum 6 + 6 = 12. This row has an asterisk.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/th>\n<th data-valign=\"top\" data-align=\"left\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1, 36<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b96ac6fa81c310eb9c1a2820776f6296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#51;&#54;&#61;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2, 18<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f7448eefebc86b9ecb99f13a295183c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#49;&#56;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3, 12<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a8acc6120a9cd92f4c73400133e1f77b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#49;&#50;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">4, 9<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ddf3bc3ae28bae64c39ca73971db148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#57;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"81\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">6, 6<\/td>\n<td data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65a7812b65af0110cb62c4b7b59c7bc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#54;&#61;&#49;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343000756\">Use 6 and 6 as the coefficients of the last terms.\u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f8f4118b36c822636db8c8b08181511_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>Check your answer.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-247651b256c7cb0e0da6af9479f7b716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#121;&#43;&#54;&#120;&#121;&#43;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#121;&#43;&#51;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"174\" style=\"vertical-align: -26px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343128752\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343128756\" data-type=\"exercise\">\n<div id=\"fs-id1168343175338\" data-type=\"problem\">\n<p id=\"fs-id1168343175340\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35812abd0ba7007ed8abab88cfdf7f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#117;&#118;&#43;&#50;&#56;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343062962\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343062964\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c822584ddf6bcfc563e3739b9dc9ea68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#52;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#55;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343194963\" data-type=\"problem\">\n<p id=\"fs-id1168343194965\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-db547ecdffe78c8f52c97ce06efb04c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#51;&#120;&#121;&#43;&#52;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343004771\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343004773\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29650ddf9f37ca270d2e5e8c9bdd09a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344555684\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344555688\" data-type=\"exercise\">\n<div id=\"fs-id1168343004771\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343132295\" data-type=\"problem\">\n<p id=\"fs-id1168343132297\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0295546f71173228da29a8a7efec5de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#114;&#120;&#45;&#57;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"111\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168342964500\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168342964505\">We need <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> in the first term of each binomial and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> in the second term. The last term of the trinomial is negative, so the factors must have opposite signs.<\/p>\n<p id=\"fs-id1168344505665\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-deecdc3ff969f447d8645dd8c42d5825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#38;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#114;&#120;&#45;&#57;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#111;&#116;&#101;&#32;&#116;&#104;&#97;&#116;&#32;&#116;&#104;&#101;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#97;&#114;&#101;&#32;&#114;&#44;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#99;&#111;&#110;&#116;&#97;&#105;&#110;&#32;&#115;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#95;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#95;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"530\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1168343130225\">Find the numbers that multiply to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<table id=\"fs-id1168344603447\" class=\"grid\" style=\"height: 58px;\" summary=\"This table has two columns. The first column is labeled factors of \u22129 and the second column is labeled sum of factors. The first row has the factors 1, negative 9 and the sum 1 + (negative 9) = negative 8. This row has an asterisk. The second row has the factors negative 1, 9 and the sum negative 1 + 9 = 8. The third row has the factors 3, negative 3 and the sum 3 + (negative 3) = 0.\" data-label=\"\">\n<thead>\n<tr style=\"height: 13px;\" valign=\"top\">\n<th style=\"height: 13px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/th>\n<th style=\"height: 13px; width: 359.119px;\" data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e86756360fa23209bcb59372e45e2449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2a39a6f9eabc1e5fbcd51a47817496c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc3e9f9c6cf0cbd0eb1b78d7afa30b7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ab83730be57528840d4f21f8f5a2f7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#57;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"height: 15px; width: 196.392px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8f99a729c7a37f3083f2bbfa4f2a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 360.028px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73e86a59d27c4436a13252059c8b5ad8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344620205\">Check your answer.Use 1, -9 as coefficients of the last terms. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f93274b25d643028e6a3ab1a9a675274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#57;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e63c3f4a3aece4db4982f7b0b38c81f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#57;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#114;&#115;&#45;&#57;&#114;&#115;&#45;&#57;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#32;&#92;&#92;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#114;&#115;&#45;&#57;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"148\" style=\"vertical-align: -23px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344296891\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343023332\" data-type=\"exercise\">\n<div id=\"fs-id1168343023334\" data-type=\"problem\">\n<p id=\"fs-id1168343023336\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-704b3e2cfc15338142fa11127f66e5f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#97;&#98;&#43;&#49;&#48;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"128\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343069911\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343069913\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-207d840c06582684b2cc8b378547fa67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#49;&#48;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344477412\" data-type=\"problem\">\n<p id=\"fs-id1168344477414\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32b808ea7bad90510b163104cf5af9bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#51;&#109;&#110;&#43;&#49;&#50;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343035769\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168343035771\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-558a1566c03a7d50c2ab1af5e93c1b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#49;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343054681\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343054684\" data-type=\"exercise\">\n<div id=\"fs-id1168343035769\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344312555\" data-type=\"problem\">\n<p id=\"fs-id1168344312557\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2629e5fbb7b3d8588d9e98d4178507d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#117;&#118;&#45;&#49;&#50;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"123\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343246623\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344600930\">We need <em data-effect=\"italics\">u<\/em> in the first term of each binomial and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> in the second term. The last term of the trinomial is negative, so the factors must have opposite signs.<\/p>\n<p id=\"fs-id1168344440611\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48744ac097fd6a3fedb81e0bb5bc47fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#32;&#38;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#117;&#118;&#45;&#49;&#50;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#111;&#116;&#101;&#32;&#116;&#104;&#97;&#116;&#32;&#116;&#104;&#101;&#32;&#102;&#105;&#114;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#97;&#114;&#101;&#32;&#117;&#44;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#99;&#111;&#110;&#116;&#97;&#105;&#110;&#32;&#118;&#46;&#125;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#95;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#95;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"547\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1168343138131\">Find the numbers that multiply to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> and add to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<table id=\"fs-id1168344579863\" class=\"grid\" style=\"height: 105px;\" summary=\"This table has two columns. The first column is labeled factors of negative12 and the second column is labeled sum of factors. The first row has the factors 1, negative 12 and the sum 1 + negative 12 = negative 11. The second row has the factors negative 1, 12 and the sum negative 1 + 12 = 11. The third row has the factors 2, negative 6 and the sum 2 + (negative 6) = negative 4. The fourth row has the factors negative 2, 6 and the sum negative 2 + 6 = 4. The fifth row has the factors 3, negative 4 and the sum 3 + (negative 4) = negative 1. The sixth row has the factors negative 3, 4 and the sum negative 3 + 4 = 1.\" data-label=\"\">\n<thead>\n<tr style=\"height: 15px;\" valign=\"top\">\n<th style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\">Factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/th>\n<th style=\"width: 320.028px; height: 15px;\" data-align=\"center\" data-valign=\"top\">Sum of factors<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70f5a3806b6defba03b6ad874f509567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9001355fd34938476ac0c80f25c79022_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf2ec31384da5049b5a7a6cfb3afbc4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#44;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49c1a8525441a24b949f3cff582472e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#49;&#50;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"102\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-179533d69e95895dfbd8e709fe504994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#44;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfe9dda07dafb1519b4af72c7ca34706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b6cb7bd123df87bfa34d0f1d2da73de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#44;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9af9e38b16590636223f1c46578997db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#54;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c02e04c5b5cff7ddce31d2aeffe6c6f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d46ab22315da05913a5fbbb683c45914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\" valign=\"top\">\n<td style=\"width: 235.483px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb23bbfc0807f7a62700e62cf257910b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#44;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 320.938px; height: 15px;\" data-align=\"center\" data-valign=\"top\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bd6ea88b80c6ab4a48e62f8b6f8cd07a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#43;&#52;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168343069930\">Note there are no factor pairs that give us <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> as a sum. The trinomial is prime.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343119792\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344599076\" data-type=\"exercise\">\n<div id=\"fs-id1168344599078\" data-type=\"problem\">\n<p id=\"fs-id1168344599080\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f76c4b6931d8ca18b3b944e31135d519_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#121;&#45;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168344437739\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168344437741\">prime<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343128972\" data-type=\"problem\">\n<p id=\"fs-id1168343128974\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31c8a9683f3b5a6644eb63f4205037ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#112;&#113;&#43;&#50;&#48;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168343054336\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168342979739\">prime<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1168344316915\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Factor trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/strong>\n<ol id=\"fs-id1168746486111\" class=\"stepwise\" type=\"1\">\n<li>Write the factors as two binomials with first terms <em data-effect=\"italics\">x<\/em>: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3970b19006c0cc8402a8327fc781643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -5px;\" \/>.<\/li>\n<li>Find two numbers <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> that<br \/>\nMultiply to <em data-effect=\"italics\">c<\/em>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fbd6bb5b853a59432595a4e23342cfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#110;&#61;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"71\" style=\"vertical-align: 0px;\" \/><br \/>\nAdd to <em data-effect=\"italics\">b<\/em>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3016e48f6b3e5e5184cd3010a2b9d479_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#43;&#110;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: -2px;\" \/><\/li>\n<li>Use <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em> as the last terms of the factors: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-612a2d96dc1eee1dfd8d2384d5741ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Factor Trinomials of the Form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/h2>\n<p id=\"fs-id1168744119122\">In the following exercises, factor each trinomial of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63724e69e8a99aa529eceb23ed0b2d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c815c5998e4f1e8f6e71dcf75125982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c3643c4fcbe397a9f1b93a87143c166_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#109;&#43;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"117\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4cf94ecebf3fd64085dcf5b11f6e31fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#98;&#43;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"102\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51798d894727e8deea43d1bb6bc70910_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#97;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-364cdcbed984891f092fe138dbb768e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#109;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fbd6b7ba78fd9952a3f4867444b46cdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#112;&#43;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27740b5b1c8a9b763dabe52cbde71255_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#120;&#43;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e85c231f51abca640162a4b38e2d619_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#57;&#110;&#43;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9832a29c700c61ed4bf62e44db5f3d54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#98;&#43;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"102\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e7418992e639667de4b2871446d54c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#97;&#43;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"114\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d13d40ee8356fdb1eb27e01033dcd50f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#49;&#117;&#43;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"125\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82b40c9869282c51ca0c7530ca8cac95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2821b9c86cebe3ccc7aaba5b3eed1a45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#51;&#113;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05c72d9b9ef2e6e303746d9d04dcebe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#56;&#120;&#43;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29eb5ebb4d2301375321dda70c5568c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#51;&#109;&#43;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5afe4f2772ccf956980f8497093a321a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffaad88ce25a5da4f0fbd7e1f0eece4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2f377fa1abfbb8a42f7a2e4b66888cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#112;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e05465e4e5d02de0bea615adf2a9fae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#110;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-797332031e81ca612cdf4278c7fa7f92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#121;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34abe9a7fbb4a891447f37ffadce99b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#118;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-703f7c4f04a6f58a1ee1fe54a96deb93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94a25b38a491ced33a54d49022715ca5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#114;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"86\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-327dc9fa7155b43bf01be7be60fd8e95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#97;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"97\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec4df713cd294c63d6b1366175cb08d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#51;&#98;&#45;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"102\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c52176c1061d4757653ba9d9af4cf110_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#119;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"104\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0609f2bf0f8903f552f5e305cbd6e4f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#116;&#45;&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7291a05983d4817bc320827d1f1819c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a994ff24e44888c499d0d2ad89fdcd2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85484b1df24265c6f86ae96c0fc6b6bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#54;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e8e2be4340c8de3b3e8bc962358287d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70ccb0dbcdeb4f66d2f65de51b9c000a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#45;&#49;&#49;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bacfd79c92ae9937d13748a5a0ebb4d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#45;&#49;&#48;&#120;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1168343007291\" data-type=\"exercise\">\n<div id=\"fs-id1168343007293\" data-type=\"problem\">\n<h2>Factor Trinomials of the Form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02db4b17730ec637e3f4c699969ade06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#121;&#43;&#99;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/h2>\n<\/div>\n<\/div>\n<p id=\"fs-id1168744271961\">In the following exercises, factor each trinomial of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02db4b17730ec637e3f4c699969ade06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#121;&#43;&#99;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f509f9f8bdc5f416364fbda3bdfea90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#112;&#113;&#43;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc5c7139c83180779a352843b4bd05a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#109;&#110;&#43;&#53;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c82eeadaa76d91a8b6a9534063e86854_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#114;&#115;&#43;&#51;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-999214eccd56d7b1e2ce3d18593331e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#117;&#118;&#43;&#50;&#52;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b075615f8857e9100adc88c31ae12cfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#109;&#110;&#43;&#50;&#48;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-623daf3abc1fb3d1dbe11dccf356394b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#112;&#113;&#43;&#54;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e9dabd39d1677fbd9bff5b831054f38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#121;&#45;&#56;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3e1624a0a67861a2a7f6b558d059af3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#112;&#113;&#45;&#54;&#53;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8915e7407dee793ab654af1f6656a4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#52;&#109;&#110;&#45;&#54;&#53;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"147\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a46345427b417f7b9144f8b3c79f1510_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#112;&#113;&#45;&#51;&#53;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e95c6cf2e6326170ed4d7e80a314247f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#97;&#98;&#45;&#50;&#52;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8f815647c4de8458399eb0456a4122e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#114;&#115;&#45;&#50;&#56;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8ad236b7639a8a8587461894cb8d2f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#45;&#49;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce73092ce06edfb304d2ad07e93766b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#117;&#118;&#45;&#50;&#52;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"123\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b0c7adbc105b6cad71e461d82e7b9f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#109;&#110;&#43;&#51;&#48;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"138\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c5d65a937c9bc16b0c09b8d4a97b23e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#99;&#100;&#43;&#49;&#56;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1168343045418\" data-type=\"exercise\">\n<h2 id=\"fs-id1168343045420\" data-type=\"problem\">Mixed Practice<\/h2>\n<\/div>\n<p id=\"fs-id1168743433329\">In the following exercises, factor each expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 140px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5cfa768ce54f16a047d30ddf88a707a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#117;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fe1a5dfb82e17273c79276c552a79b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#119;&#45;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"103\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2da61c5acc94736edf320e635200c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#120;&#45;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34256d505998a8f92ddf3865ced8d7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#49;&#121;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cfa873a6882192b27fef3822d23b3130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#48;&#114;&#115;&#43;&#54;&#52;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2dd9523fdd9f3c6f01b31c4419f2ab25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#120;&#121;&#43;&#54;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f064bb0206d0ecf8ab7fee36a2d100c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#52;&#107;&#43;&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"115\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-555f2891d24bede60421e0719e690169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#57;&#109;&#43;&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77951f8603d5c47a6aa62dd406d82ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#121;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bf2069b790a0c4a5492038804d25486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#122;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7fbf9498644ac637c4dca53f2d1466c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#109;&#110;&#45;&#53;&#54;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"129\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-caf61a877008e44a11df159de5dd7371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#57;&#113;&#114;&#45;&#57;&#54;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c67d01e4bede5686850b56122d01fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#55;&#117;&#118;&#43;&#51;&#48;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b029cd89b08be4a653512c337a902e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#49;&#109;&#110;&#43;&#51;&#48;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71a5caa620788b8b3988059e7105946b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#99;&#100;&#43;&#50;&#54;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa6a5b7a762924cef1a24d38f2f25664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#114;&#115;&#43;&#51;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">67.<strong data-effect=\"bold\"> Consecutive integers<\/strong> Deirdre is thinking of two consecutive integers whose product is 56. The trinomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e90898b566b0d7609ec95e071f31cc38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/> describes how these numbers are related. Factor the trinomial.<\/td>\n<td style=\"width: 50%;\">68.<strong data-effect=\"bold\"> Consecutive integers<\/strong> Deshawn is thinking of two consecutive integers whose product is 182. The trinomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f202685ebae58c4faf7a6e2cb73fd193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#49;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/> describes how these numbers are related. Factor the trinomial.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">69. Many trinomials of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/> factor into the product of two binomials <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-612a2d96dc1eee1dfd8d2384d5741ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/>. Explain how you find the values of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em>.<\/td>\n<td style=\"width: 50%;\">70. How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> may be positive or negative numbers?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. Will factored <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66d931a636e5d477f7869c9407fde46c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87ead409205c2d6fac57451aa4fcec2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/>. Bill factored it as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e2f52f8aec7a8d861ea598ded307d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/>. Phil factored it as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e342cd82aa8314e37fd0d056a1616dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/>. Who is correct? Explain why the other two are wrong.<\/td>\n<td style=\"width: 50%;\">72. Look at <a class=\"autogenerated-content\" href=\"#fs-id1168344083254\">(Figure)<\/a>, where we factored <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75007ce6e065b4b2cb46d40dfcb2bc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#121;&#43;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/>. We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">1.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ea7b2ac1d5806de925a157da3cb9a8cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-131aa607248ad4e02d7f23f557239028_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e8a360e26bf7f24c0106e7ec495e76e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb68d89e2f4eaf5380d8d2c4ecf90299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e24e1e322ddf1d8621b24366f603c82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f71be17e4892e848d7a4110fad73a4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0df50359022c5bb7946f87e19b54eaf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-534a38338261fc0032d992224f04c575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b105ab4fe4a05b269e83cde642371315_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d90f6cc209a7c285bd7da3f94951f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f9e0baa3930b588bc699ca2cf4e963ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-45a830e0afb867214900385dde36da1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df3a568c9f50f70302c2efe7660e0933_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-733a5a706cb0040b4d04126002536e73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">29. prime<\/td>\n<td style=\"width: 50%; height: 16px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71c546f918f08ea1b2d15bd988882e6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d7df8c46c7938adc4a70005aaaf0fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-354ee609ea61ee16ca0483307fba8dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#50;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-11515962320a197908f49579b5fa21e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#51;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#43;&#49;&#50;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"132\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 16px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ad985fdf7b93991ba271a93a4e86da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#49;&#48;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d74d49c669a27edfd790deb6cf7437e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#48;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87221a3b707f1fd2f9af4ded4405b4c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#54;&#53;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15322acc9adc219f4a56d83786ed991a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#56;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#51;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">47. prime<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. prime<\/td>\n<td style=\"width: 50%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-053e1c26f08866b6e8a1e8e2a9588746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18188988738215a54dc98ada38fed3aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3fa10e33eb2b2c7a0a45d3fb10e6445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#52;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#49;&#54;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"132\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de1325dfe94d1aa114e275fbbc865923_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#43;&#51;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">59. prime<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9bb5c33022c87a4ba3e802a486e3debe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#56;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#55;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34db30c2a79d2e3bea47bf6e5276f83a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#49;&#53;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#50;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. prime<\/td>\n<td style=\"width: 50%;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5150b4a8df902031877bafa69d443a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69. Answers may vary<\/td>\n<td style=\"width: 50%;\">71. Answers may vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cFactor Trinomials of the Form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3995eb3274bb5bf3d3e8fb22d033b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#98;&#120;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2265","chapter","type-chapter","status-publish","hentry"],"part":2016,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2265","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2265\/revisions"}],"predecessor-version":[{"id":2523,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2265\/revisions\/2523"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/2016"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2265\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=2265"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=2265"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=2265"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=2265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}