{"id":2258,"date":"2020-08-21T19:42:39","date_gmt":"2020-08-21T23:42:39","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/greatest-common-factor-and-factor-by-grouping\/"},"modified":"2025-09-22T19:26:25","modified_gmt":"2025-09-22T23:26:25","slug":"greatest-common-factor-and-factor-by-grouping","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/greatest-common-factor-and-factor-by-grouping\/","title":{"raw":"8.4  Greatest Common Factor and Factor by Grouping","rendered":"8.4  Greatest Common Factor and Factor by Grouping"},"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>Find the greatest common factor of two or more expressions<\/li>\n \t<li>Factor the greatest common factor from a polynomial<\/li>\n \t<li>Factor by grouping<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Find the Greatest Common Factor of Two or More Expressions<\/h1>\n<p id=\"fs-id1168345388781\">Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring.<\/p>\n<span id=\"fs-id1168345656426\" data-type=\"media\" data-alt=\"This figure has two factors being multiplied. They are 8 and 7. Beside this equation there are other factors multiplied. They are 2x and (x+3). The product is given as 2x^2 plus 6x. Above the figure is an arrow towards the right with multiply inside. Below the figure is an arrow to the left with factor inside.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_Elem20Alg_Figure_07_01_001_img_new.jpg\" alt=\"This figure has two factors being multiplied. They are 8 and 7. Beside this equation there are other factors multiplied. They are 2x and (x+3). The product is given as 2x^2 plus 6x. Above the figure is an arrow towards the right with multiply inside. Below the figure is an arrow to the left with factor inside.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1168345677793\">We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the greatest common factor of two or more expressions. The method we use is similar to what we used to find the LCM.<\/p>\n\n<div id=\"fs-id1168345291091\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Greatest Common Factor<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nThe <span class=\"no-emphasis\" data-type=\"term\">greatest common factor<\/span> (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168342171304\">First we\u2019ll find the GCF of two numbers.<\/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 Find the Greatest Common Factor of Two or More Expressions<\/div>\n<div id=\"fs-id1168345255994\" data-type=\"exercise\">\n<div id=\"fs-id1168345192684\" data-type=\"problem\">\n<p id=\"fs-id1168341973334\">Find the GCF of 54 and 36<\/p>\n\n<\/div>\n<div id=\"fs-id1168345424484\" 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-id1168345635362\" data-type=\"media\" data-alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, factor each coefficient into primes and write all variables with exponents in expanded form. The second column in the first row has \u201cfactor 54 and 36\u201d. The third column in the first row has 54 and 36 factored with factor trees. The prime factors of 54 are circled and are 3, 3, 2, and3. The prime factors of 36 are circled and are 2,3,2,3.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002a_img_new.jpg\" alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, factor each coefficient into primes and write all variables with exponents in expanded form. The second column in the first row has \u201cfactor 54 and 36\u201d. The third column in the first row has 54 and 36 factored with factor trees. The prime factors of 54 are circled and are 3, 3, 2, and3. The prime factors of 36 are circled and are 2,3,2,3.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345342690\" data-type=\"media\" data-alt=\"The second row has the second step of \u201cin each column, circle the common factors. The second column in the second row has the statement \u201ccircle the 2, 3 and 3 that are shared by both numbers\u201d. The third column in the second row has the prime factors of 36 and 54 in rows above each other. The common factors of 2, 3, and 3 are circled.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002b_img_new.jpg\" alt=\"The second row has the second step of \u201cin each column, circle the common factors. The second column in the second row has the statement \u201ccircle the 2, 3 and 3 that are shared by both numbers\u201d. The third column in the second row has the prime factors of 36 and 54 in rows above each other. The common factors of 2, 3, and 3 are circled.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345425779\" data-type=\"media\" data-alt=\"The third row has the step \u201cbring down the common factors that all expressions share\u201d. The second column in the third row has \u201cbring down the 2,3, and 3 then multiply\u201d. The third column in the third row has \u201cGCF = 2 times 3 times 3\u201d.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002c_img_new.jpg\" alt=\"The third row has the step \u201cbring down the common factors that all expressions share\u201d. The second column in the third row has \u201cbring down the 2,3, and 3 then multiply\u201d. The third column in the third row has \u201cGCF = 2 times 3 times 3\u201d.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345434590\" data-type=\"media\" data-alt=\"The fourth row has the fourth step \u201cmultiply the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has \u201cGCF = 18\u201d and \u201cthe GCF of 54 and 36 is 18\u201d.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002d_img_new.jpg\" alt=\"The fourth row has the fourth step \u201cmultiply the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has \u201cGCF = 18\u201d and \u201cthe GCF of 54 and 36 is 18\u201d.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1168345633976\">Notice that, because the GCF is a factor of both numbers, 54 and 36 can be written as multiples of 18<\/p>\n\n<div id=\"fs-id1168745570074\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}54=18\\cdot 3\\\\ 36=18\\cdot 2\\end{array}\\)<\/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 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341907611\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345670292\" data-type=\"exercise\">\n<div id=\"fs-id1168345743063\" data-type=\"problem\">\n<p id=\"fs-id1168345329454\">Find the GCF of 48 and 80.<\/p>\n\n<\/div>\n<div id=\"fs-id1168341916032\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345251014\">16<\/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 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345522058\" data-type=\"problem\">\n<p id=\"fs-id1168345300785\">Find the GCF of 18 and 40.<\/p>\n\n<\/div>\n<div id=\"fs-id1168345450073\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345509731\">2<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345487595\">We summarize the steps we use to find the GCF below.<\/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\nFind the Greatest Common Factor (GCF) of two expressions\n<ol id=\"fs-id1168741892867\" class=\"stepwise\" type=\"1\">\n \t<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n \t<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n \t<li>Bring down the common factors that all expressions share.<\/li>\n \t<li>Multiply the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\nIn the first example, the GCF was a constant. In the next two examples, we will get variables in the greatest common factor.\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-id1168345647941\" data-type=\"problem\">\n<p id=\"fs-id1168345227453\">Find the greatest common factor of \\(27{x}^{3}\\) and \\(18{x}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345557943\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172184762201\" class=\"unnumbered unstyled\" summary=\"This image has two terms above each other with the factors to the right. The first term is 27 x three times and has factors 3, 3, 3, x, x, x. The second term is 18 x 4 times and has factors 2, 3, 3, x, x, x, x. Below these two rows is a line. Below the line are the two statements \u201cGCF = 3 times 3 times x times x times x\u201d and \u201cG C F = 9 x 3 times\u201d. Below this is the statement \u201cthe G C F of 27 x 3 times and 18 x 4 times is 9 x 3 times\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td><span id=\"eip-id1172184762222\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Bring down the common factors.<\/td>\n<td><span id=\"eip-id1172184770130\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply the factors.<\/td>\n<td><span id=\"eip-id1172184770147\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The GCF of \\(27{x}^{3}\\) and \\(18{x}^{4}\\) is \\(9{x}^{3}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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<div id=\"fs-id1168345622514\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345367998\" data-type=\"exercise\">\n<div id=\"fs-id1168345240940\" data-type=\"problem\">\n<p id=\"fs-id1168345363065\">Find the GCF: \\(12{x}^{2},18{x}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345191223\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345414926\">\\(3{x}^{2}\\)<\/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-id1168345357691\" data-type=\"problem\">\n<p id=\"fs-id1168345445832\">Find the GCF: \\(16{y}^{2},24{y}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345442278\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168341840802\">\\(8{y}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341973453\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345578746\" data-type=\"exercise\">\n<div id=\"fs-id1168345442278\" data-type=\"solution\">\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-id1168345646517\" data-type=\"problem\">\n<p id=\"fs-id1168345195586\">Find the GCF of \\(4{x}^{2}y,6x{y}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345689915\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187711032\" class=\"unnumbered unstyled can-break\" style=\"height: 123px;\" summary=\"This image has two terms above each other with the factors to the right. The first term is 4 x squared times y and has factors 2, 2, x, x, y. The second term is 6 times x times y cubed and has factors 2, 3, x, y, y, y. Below these two rows is a line. Below the line are two statements \u201cG C F = 2 times x times y\u201d and \u201cG C F = 2 x y\u201d. Below this is the statement \u201cthe G C F of 4 times x squared times y and 6 times x times y cubed is 2 x y\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 73px;\">\n<td style=\"height: 73px; width: 826.406px;\">Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td style=\"height: 73px; width: 404.406px;\"><span id=\"eip-id1172188156282\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 826.406px;\">Bring down the common factors.<\/td>\n<td style=\"height: 18px; width: 404.406px;\"><span id=\"eip-id1172188156299\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 826.406px;\">Multiply the factors.<\/td>\n<td style=\"height: 18px; width: 404.406px;\"><span id=\"eip-id1172188156316\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 826.406px;\"><\/td>\n<td style=\"height: 14px; width: 404.406px;\">The GCF of \\(4{x}^{2}y\\) and \\(6x{y}^{3}\\) is \\(2\\mathrm{xy}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\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-id1168345434578\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345357736\" data-type=\"exercise\">\n<div id=\"fs-id1168345742331\" data-type=\"problem\">\n<p id=\"fs-id1168345230263\">Find the GCF: \\(6a{b}^{4},8{a}^{2}b\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345420190\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345377018\">\\(2ab\\)<\/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-id1168345677485\" data-type=\"problem\">\n<p id=\"fs-id1168345262355\">Find the GCF: \\(9{m}^{5}{n}^{2},12{m}^{3}n\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345415642\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345553226\">\\(3{m}^{3}n\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345426967\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345370552\" data-type=\"exercise\">\n<div id=\"fs-id1168345415642\" data-type=\"solution\">\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-id1168345292398\" data-type=\"problem\">\n<p id=\"fs-id1168345644039\">Find the GCF of: \\(21{x}^{3},9{x}^{2},15x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345675934\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172185570976\" class=\"unnumbered unstyled\" style=\"height: 151px;\" summary=\"This image has three terms above each other with the factors to the right. The first term is 21 x three times and has factors 3,7, x, x, x. The second term is 9 x 2 times and has factors 3, 3, x, x. The third term is 15 x and has factors 3, 5, x. Below these three rows is a line. Below the line are the two statements \u201cG C F = 3 times x\u201d and \u201cG C F = 3 times x\u201d. Below this is the statement \u201cthe G C F of 21 x 3 times, 9 x 2 times, and 15 x is 3 x\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 109px;\">\n<td style=\"height: 109px; width: 826.406px;\">Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td style=\"height: 109px; width: 372.406px;\"><span id=\"eip-id1172185570997\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 826.406px;\">Bring down the common factors.<\/td>\n<td style=\"height: 15px; width: 372.406px;\"><span id=\"eip-id1172185571014\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 13px;\">\n<td style=\"height: 13px; width: 826.406px;\">Multiply the factors.<\/td>\n<td style=\"height: 13px; width: 372.406px;\"><span id=\"eip-id1172185571030\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 826.406px;\"><\/td>\n<td style=\"height: 14px; width: 372.406px;\">The GCF of \\(21{x}^{3}\\), \\(9{x}^{2}\\) and \\(15x\\) is \\(3x\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345565463\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345217896\" data-type=\"exercise\">\n<div id=\"fs-id1168345194498\" data-type=\"problem\">\n<p id=\"fs-id1168345743857\">Find the greatest common factor: \\(25{m}^{4},35{m}^{3},20{m}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345511096\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345635282\">\\(5{m}^{2}\\)<\/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 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345451904\" data-type=\"problem\">\n<p id=\"fs-id1168345228410\">Find the greatest common factor: \\(14{x}^{3},70{x}^{2},105x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345671388\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345425124\">\\(7x\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Factor the Greatest Common Factor from a Polynomial<\/h1>\n<p id=\"fs-id1168345261365\">Just like in arithmetic, where it is sometimes useful to represent a number in factored form (for example, 12 as \\(2\\cdot 6\\) or \\(3\\cdot 4)\\), in algebra, it can be useful to represent a polynomial in factored form. One way to do this is by finding the GCF of all the terms. Remember, we multiply a polynomial by a monomial as follows:<\/p>\n\n<div id=\"fs-id1168345251904\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cc} 2\\left(x+7\\right)\\qquad &amp; \\quad \\text{factors}\\\\2\\cdot x+2\\cdot 7 &amp; \\\\ 2x+14 \\qquad &amp; \\quad \\text{product}\\end{array}\\)<\/div>\n<p id=\"fs-id1168345420818\">Now we will start with a product, like \\(2x+14\\), and end with its factors, \\(2\\left(x+7\\right)\\). To do this we apply the Distributive Property \u201cin reverse.\u201d<\/p>\n<p id=\"fs-id1168345195281\">We state the Distributive Property here just as you saw it in earlier chapters and \u201cin reverse.\u201d<\/p>\n\n<div id=\"fs-id1168345744805\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Distributive Property<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168345274390\">If \\(a,b,c\\) are real numbers, then<\/p>\n\n<div id=\"fs-id1168345230029\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccc}a\\left(b+c\\right)=ab+ac\\qquad \\quad &amp;\u00a0 \\text{and}\\qquad \\quad &amp; ab+ac=a\\left(b+c\\right)\\end{array}\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345397940\">The form on the left is used to multiply. The form on the right is used to factor.<\/p>\n\n<\/div>\n<p id=\"fs-id1168345560598\">So how do you use the Distributive Property to factor a polynomial? You just find the GCF of all the terms and write the polynomial as a product!<\/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 data-type=\"title\">How to Factor the Greatest Common Factor from a Polynomial<\/div>\n<div id=\"fs-id1168345406988\" data-type=\"exercise\">\n<div id=\"fs-id1168341973830\" data-type=\"problem\">\n<p id=\"fs-id1168345675931\">Factor: \\(4x+12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345429720\" 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-id1168345276045\" data-type=\"media\" data-alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, \u201cFind the G C F of all the terms of the polynomial\u201d. The second column in the first row has \u201cfind the G C F of 4 x and 12\u201d. The third column in the first row has 4 x factored as 2 times 2 times x and below it 18 factored as 2 times 2 times 3. Then, below the factors are the statements, \u201cG C F = 2 times 2\u201d and \u201cG C F = 4\u201d.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005a_img_new.jpg\" alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, \u201cFind the G C F of all the terms of the polynomial\u201d. The second column in the first row has \u201cfind the G C F of 4 x and 12\u201d. The third column in the first row has 4 x factored as 2 times 2 times x and below it 18 factored as 2 times 2 times 3. Then, below the factors are the statements, \u201cG C F = 2 times 2\u201d and \u201cG C F = 4\u201d.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345347355\" data-type=\"media\" data-alt=\"The second row has the second step \u201crewrite each term as a product using the G C F\u201d. The second column in the second row has the statement \u201cRewrite 4 x and 12 as products of their G C F, 4\u201d Then the two equations 4 x = 4 times x and 12 = 4 times 3. The third column in the second row has the expressions 4x + 12 and below this 4 times x + 4 times 3.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005b_img_new.jpg\" alt=\"The second row has the second step \u201crewrite each term as a product using the G C F\u201d. The second column in the second row has the statement \u201cRewrite 4 x and 12 as products of their G C F, 4\u201d Then the two equations 4 x = 4 times x and 12 = 4 times 3. The third column in the second row has the expressions 4x + 12 and below this 4 times x + 4 times 3.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345270344\" data-type=\"media\" data-alt=\"The third row has the step \u201cUse the reverse distributive property to factor the expression\u201d. The second column in the third row is blank. The third column in the third row has \u201c4(x + 3)\u201d.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005c_img_new.jpg\" alt=\"The third row has the step \u201cUse the reverse distributive property to factor the expression\u201d. The second column in the third row is blank. The third column in the third row has \u201c4(x + 3)\u201d.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345432733\" data-type=\"media\" data-alt=\"The fourth row has the fourth step \u201ccheck by multiplying the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has three expressions. The first is 4(x + 3), the second is 4 times x + 4 times 3. The third is 4 x + 12.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005d_img_new.jpg\" alt=\"The fourth row has the fourth step \u201ccheck by multiplying the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has three expressions. The first is 4(x + 3), the second is 4 times x + 4 times 3. The third is 4 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 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345276005\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345688289\" data-type=\"exercise\">\n<div id=\"fs-id1168345300927\" data-type=\"problem\">\n<p id=\"fs-id1168345465917\">Factor: \\(6a+24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345357504\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345228984\">\\(6\\left(a+4\\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-id1168345500408\" data-type=\"problem\">\n<p id=\"fs-id1168345251303\">Factor: \\(2b+14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345192702\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345219462\">\\(2\\left(b+7\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\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\nFactor the greatest common factor from a polynomial.\n<ol>\n \t<li>Find the GCF of all the terms of the polynomial.<\/li>\n \t<li>Rewrite each term as a product using the GCF.<\/li>\n \t<li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345448814\" data-type=\"note\">\n<div data-type=\"title\">Factor as a Noun and a Verb<\/div>\n<p id=\"fs-id1168341907170\">We use \u201cfactor\u201d as both a noun and a verb.<\/p>\n<span id=\"fs-id1168345508580\" data-type=\"media\" data-alt=\"This figure has two statements. The first statement has \u201cnoun\u201d. Beside it the statement \u201c7 is a factor of 14\u201d labeling the word factor as the noun. The second statement has \u201cverb\u201d. Beside this statement is \u201cfactor 3 from 3a + 3 labeling factor as the verb.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_017_img_new.jpg\" alt=\"This figure has two statements. The first statement has \u201cnoun\u201d. Beside it the statement \u201c7 is a factor of 14\u201d labeling the word factor as the noun. The second statement has \u201cverb\u201d. Beside this statement is \u201cfactor 3 from 3a + 3 labeling factor as the verb.\" data-media-type=\"image\/jpeg\"><\/span>\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-id1168341862477\" data-type=\"problem\">\n<p id=\"fs-id1168345434116\">Factor: \\(5a+5\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345292167\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172185559033\" class=\"unnumbered unstyled\" summary=\"This figure has the steps for factoring 5a + 5. First, is finding the G C F of 5 a and 5. The first row has the equation 5 a equals 5 times a. Below this there is the equation 5 equals 5. In these two equations, the 5\u2019s are circled on the right hand side. Below these equations is the statement, G C F equals 5. Below this is the expression 5 a + 5. Below this, the terms of the expression are written with factors, 5 times a + 5 times 1. Below this is the expression 5(a + 1), showing the 5 factored from the expression. Below this, the factoring is checked by multiplying 5(a + 1). The step below this is 5 times a + 5 times 1. Then, the answer, 5a + 5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of 5<em data-effect=\"italics\">a<\/em> and 5.<\/td>\n<td><span id=\"eip-id1172185559054\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172185559069\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172186035559\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Distributive Property \"in reverse\" to factor the GCF.<\/td>\n<td><span id=\"eip-id1172186035575\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying the factors to get the orginal polynomial.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5\\left(a+1\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5\\cdot a+5\\cdot 1\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5a+5\\checkmark \\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345436261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345665214\" data-type=\"exercise\">\n<div id=\"fs-id1168345216274\" data-type=\"problem\">\n<p id=\"fs-id1168345550230\">Factor: \\(14x+14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345427982\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345726539\">\\(14\\left(x+1\\right)\\)<\/p>\n\n<\/details><\/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 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345517802\" data-type=\"problem\">\n<p id=\"fs-id1168345216876\">Factor: \\(12p+12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345423512\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168341962889\">\\(12\\left(p+1\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345448711\">The expressions in the next example have several factors in common. Remember to write the GCF as the product of all the common factors.<\/p>\n\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-id1168341864057\" data-type=\"problem\">\n<p id=\"fs-id1168345507877\">Factor: \\(12x-60\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345202847\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172183494582\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for factoring 12 x minus 60. First, is finding the GCF of 12 x and 60. Two equations are written. The first equation has the factors of 12 x = 2 times 2 times 3 times x. Below this, the equation 60 = 2 times 2 times 3 times 5. In these equations the common factors of 2, 2, and 3 are circled. Below these two equations is are the statements G C F = 2 times 2 times 3 and G C F = 12. Then, the expression 12 x minus 60 is written. Below is the expression with 12 factored from both terms, 12 times x minus 12 times 5. Then, the factoring is written 12 times x \u2013minus 5, with x minus 5 in parentheses. Finally, the factoring is checked with multiplying 12 times x minus 5, x minus 5 in parentheses. The statement, 12 times x minus 12 times 5. Below this is the product 12 x minus 60.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of 12<em data-effect=\"italics\">x<\/em> and 60.<\/td>\n<td><span id=\"eip-id1172183494602\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172183494617\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172188156364\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172188156380\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying the factors.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(12\\left(x-5\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(12\\cdot x-12\\cdot 5\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(12x-60\\checkmark \\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345723945\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345557216\" data-type=\"exercise\">\n<div id=\"fs-id1168345442218\" data-type=\"problem\">\n<p id=\"fs-id1168345302689\">Factor: \\(18u-36\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345466169\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168342170087\">\\(8\\left(u-2\\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 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345269905\" data-type=\"problem\">\n<p id=\"fs-id1168345621361\">Factor: \\(30y-60\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168342048497\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345398080\">\\(30\\left(y-2\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345450727\">Now we\u2019ll factor the greatest common factor from a trinomial. We start by finding the GCF of all three terms.<\/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-id1168345530229\" data-type=\"problem\">\n<p id=\"fs-id1168345483991\">Factor: \\(4{y}^{2}+24y+28\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345574716\" 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-id1168345429115\">We start by finding the GCF of all three terms.<\/p>\n\n<table id=\"eip-id1172187652496\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for factoring 4 y squared plus 24 y plus 28. The first step is finding the G C F of 4 times y squared, 24 times y and 28. There are three equations written with factors. The first is 4 times y squared equals 2 times 2 times y times y. The second is 2 times 2 times 2 times 3 times y. The third is 2 times 2 times 7. In these equations the common factors of 2 and 2 are circled. Under these equations there is the statement G C F equals 2 times 2 and the statement G C F = 4. The next row has the polynomial 4 y squared plus 24 y plus 28. Under this, each term has the factor of 4, written 4 times y squared plus 4 times 6 y plus 4 times 7. The next expression has the 4 factored out, 4( y squared plus 6 y plus 7). Under this the factoring is checked by multiplying 4 (y squared plus 6 y plus7). The product is 4 times y squared + 24 y + 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of \\(4{y}^{2}\\), \\(24y\\) and 28.<\/td>\n<td><span id=\"eip-id1172187652534\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187652549\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172187652566\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187652582\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(4\\left({y}^{2}+6y+7\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(4\\cdot {y}^{2}+4\\cdot 6y+4\\cdot 7\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(4{y}^{2}+24y+28\\checkmark\\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345622986\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345508556\" data-type=\"exercise\">\n<div id=\"fs-id1168345508558\" data-type=\"problem\">\n<p id=\"fs-id1168345741313\">Factor: \\(5{x}^{2}-25x+15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345398436\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345398438\">\\(5\\left({x}^{2}-5x+3\\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 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345215798\" data-type=\"problem\">\n<p id=\"fs-id1168345677606\">Factor: \\(3{y}^{2}-12y+27\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345418264\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345418266\">\\(3\\left({y}^{2}-4y+9\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345529877\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341861952\" data-type=\"exercise\">\n<div id=\"fs-id1168345418264\" 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-id1168341918996\" data-type=\"problem\">\n<p id=\"fs-id1168341918999\">Factor: \\(5{x}^{3}-25{x}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168342169956\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187580327\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps for factoring 5 times x 3 times minus 25 x squared. First, is finding the G C F of 5 times x 3 times and 25 x squared. Two equations are written. The first equation has the factors of 5 times x 3 times equals 5 times x times x times x. Below this, the equation 25 times x squared equals 5 times 5 times x times x. In these equations the common factors of 5, x, and x are circled. Below these two equations is are the statements G C F = 5 times x times x and G C F = 5 x squared. Then, the expression 5 times x 3 times minus 25 x squared is written. Below is the expression with 5 times x squared factored from both terms, 5 x squared times x minus 5 x squared times 5. Then, the factoring is written 5 x squared times (x minus 5). Finally, the factoring is checked with multiplying 5 times x squared times (x minus 5). The statement, 5 x squared times x minus 5 x squared times 5. Below this is the product 5 x 3 \u2013 25 x 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of \\(5{x}^{3}\\) and \\(25{x}^{2}\\).<\/td>\n<td><span id=\"eip-id1172187218288\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187218304\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term.<\/td>\n<td><span id=\"eip-id1172187218320\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187218337\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5{x}^{2}\\left(x-5\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5{x}^{2}\\cdot x-5{x}^{2}\\cdot 5\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(5{x}^{3}-25{x}^{2}\\checkmark \\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n&nbsp;\n\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-id1168341901909\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341955830\" data-type=\"exercise\">\n<div id=\"fs-id1168341955832\" data-type=\"problem\">\n<p id=\"fs-id1168345419057\">Factor: \\(2{x}^{3}+12{x}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345461759\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345461762\">\\(2{x}^{2}\\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 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345638669\" data-type=\"problem\">\n<p id=\"fs-id1168345638672\">Factor: \\(6{y}^{3}-15{y}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168342170077\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168342170079\">\\(3{y}^{2}\\left(2y-5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345530201\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345638667\" data-type=\"exercise\">\n<div id=\"fs-id1168342170077\" data-type=\"solution\">\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-id1168345542420\" data-type=\"problem\">\n<p id=\"fs-id1168345542422\">Factor: \\(21{x}^{3}-9{x}^{2}+15x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341962958\" 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-id1168341902398\">In a previous example we found the GCF of \\(21{x}^{3},9{x}^{2},15x\\) to be \\(3x\\).<\/p>\n\n<table id=\"eip-id1172187863365\" class=\"grid\" summary=\"This figure shows the steps to factoring 21 x 3 minus 9 x 2 +15 x. The G C F is given as 3 x. The first step writes the terms of the polynomial with 3 x factored from each, 3 x times 7 x 2 minus 3 x times 3 x + 3 x times 5. Then, the 3 x is factored for the answer, 3 x times (7 x 2 minus 3 x plus 5). Then, below the factored form the answer is checked by multiplying 3 x times (7 x 2 minus 3 x plus 5). Giving the product, 21 x 3 minus 9 x 2 plus 15 x.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187863384\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term using the GCF, 3<em data-effect=\"italics\">x<\/em>.<\/td>\n<td><span id=\"eip-id1172187863401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187863417\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(3x\\left(7{x}^{2}-3x+5\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(3x\\cdot 7{x}^{2}-3x\\cdot 3x+3x\\cdot 5\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(21{x}^{3}-9{x}^{2}+15x\\checkmark\\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345430922\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345434541\" data-type=\"exercise\">\n<div id=\"fs-id1168345434543\" data-type=\"problem\">\n<p id=\"fs-id1168345434545\">Factor: \\(20{x}^{3}-10{x}^{2}+14x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341951011\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168341951013\">\\(2x\\left(10{x}^{2}-5x+7\\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-id1168345430714\" data-type=\"problem\">\n<p id=\"fs-id1168345430716\">Factor: \\(24{y}^{3}-12{y}^{2}-20y\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345741381\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345741383\">\\(4y\\left(6{y}^{2}-3y-5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342170303\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342170306\" data-type=\"exercise\">\n<div id=\"fs-id1168345741381\" 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-id1168345669993\" data-type=\"problem\">\n<p id=\"fs-id1168345526582\">Factor: \\(8{m}^{3}-12{m}^{2}n+20m{n}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341862559\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172186658692\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to factor 8 m 3 minus 12 m 2 n plus 20 m n 2. First, the G C F of the terms 8 m 3, 12 m 2 n, and 20 m n 2 are found. These terms are written in rows factored. The rows are, 8 m 3 = 2 times 2 times 2 times m times m times m. The second row has 12 m 2 n = 2 times 2 times 3 times m times m times n. The third row is 20 m 2 n = 2 times 2 times 5 times m times n times n. The common factors of all three terms are circled, 2, 2, m. Below these rows is the statement G C F = 2 times 2 times m and the statement G C F = 4 m. Below this is the polynomial 8 m 3 minus 12 m 2 n plus 20 m n 2, then the terms with 4 m factored from each. 4 m times 2 m 2 minus 4 m times 3m n plus 4 m times 5 n 2. Below this is the factored polynomial 4 m times (2 m 2 minus 3m n plus 5 n 2). Then the factoring is checked by multiplying 4 m times (2 m 2 minus 3 m n plus 5 n 2), giving the product 8 m 3 minus 12 m 2 n plus 20 m n 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of \\(8{m}^{3}\\), \\(12{m}^{2}n\\), \\(20m{n}^{2}\\).<\/td>\n<td><span id=\"eip-id1172189038688\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189038704\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term.<\/td>\n<td><span id=\"eip-id1172187574020\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172189040472\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(4m\\left(2{m}^{2}-3mn+5{n}^{2}\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(4m\\cdot 2{m}^{2}-4m\\cdot 3mn+4m\\cdot 5{n}^{2}\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(8{m}^{3}-12{m}^{2}n+20m{n}^{2}\\checkmark\\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345560110\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345436546\" data-type=\"exercise\">\n<div id=\"fs-id1168345436548\" data-type=\"problem\">\n<p id=\"fs-id1168345530697\">Factor: \\(9x{y}^{2}+6{x}^{2}{y}^{2}+21{y}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345540728\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345540730\">\\(3{y}^{2}\\left(3x+2{x}^{2}+7y\\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 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345455411\" data-type=\"problem\">\n<p id=\"fs-id1168345455413\">Factor: \\(3{p}^{3}-6{p}^{2}q+9p{q}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345409484\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345409486\">\\(3p\\left({p}^{2}-2pq+3{q}^{2}\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345522910\">When the leading coefficient is negative, we factor the negative out as part of the GCF.<\/p>\n\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-id1168345544292\" data-type=\"problem\">\n<p id=\"fs-id1168345544294\">Factor: \\(-8y-24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345670114\" 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-id1168341890600\">When the leading coefficient is negative, the GCF will be negative.<\/p>\n\n<table id=\"eip-id1172187954751\" class=\"grid\" style=\"height: 247px;\" summary=\"This figure shows the steps to factor negative 8 y minus 24. The first step ignores the negative sign and finds the G C F of the two terms 8 y and 24. These factors are written in two rows. The first row is 8 y = 2 times 2 times 2 times y. The second row is 24 = 2 times 2 times 2 times 3. The common factors in these two rows are circled 2, 2, 2. Below these rows is the statement G C F = 2 times 2 times 2 and the statement G C F = 8. Below this is the expression negative 8 y \u2013 24. Then each term is factored negative 8 times y plus negative 8 times 3. The factored expression is written negative 8 times (y plus 3). Under this the expression negative 8 times (y plus 3) is multiplied to check. The product is negative 8 y minus 24.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 128px;\">\n<td style=\"height: 128px; width: 965.483px;\">Ignoring the signs of the terms, we first find the GCF of 8<em data-effect=\"italics\">y<\/em> and 24 is 8. Since the expression \u22128<em data-effect=\"italics\">y<\/em> \u2212 24 has a negative leading coefficient, we use \u22128 as the GCF.<\/td>\n<td style=\"height: 128px; width: 159.119px;\"><span id=\"eip-id1172187954772\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"height: 40px; width: 965.483px;\" data-valign=\"top\">Rewrite each term using the GCF.<\/td>\n<td style=\"height: 40px; width: 159.119px;\"><span id=\"eip-id1172187954788\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\n<span id=\"eip-id1172183298209\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 965.483px;\">Factor the GCF.<\/td>\n<td style=\"height: 19px; width: 159.119px;\"><span id=\"eip-id1172183298226\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\">Check.<\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\">\\(-8\\left(y+3\\right)\\)<\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\">\\(-8\\cdot y+\\left(-8\\right)\\cdot 3\\)<\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\">\\(-8y-24\\checkmark\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345676373\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345676376\" data-type=\"exercise\">\n<div id=\"fs-id1168345695257\" data-type=\"problem\">\n<p id=\"fs-id1168345695259\">Factor: \\(-16z-64\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345486693\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345486695\">\\(-8\\left(8z+8\\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 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345406591\" data-type=\"problem\">\n<p id=\"fs-id1168345406593\">Factor: \\(-9y-27\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341857624\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345530237\">\\(-9\\left(y+3\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345517560\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345406589\" data-type=\"exercise\">\n<div id=\"fs-id1168341857624\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345517773\" data-type=\"problem\">\n<p id=\"fs-id1168345525318\">Factor: \\(-6{a}^{2}+36a\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345453838\" 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-id1168342171012\">The leading coefficient is negative, so the GCF will be negative.?<\/p>\n\n<table id=\"eip-id1172183451275\" class=\"grid\" summary=\"This figure shows the steps to factor negative 6 a 2 plus 36 a. The first step ignores the negative sign and finds the G C F of the two terms 6 a 2 and 36 a. These factors are written in two rows. The first row is 6 a 2 = 2 times 3 times a times a. The second row is 36 a = 2 times 2 times 3 times 3 times a. The common factors in these two rows are circled 2, 3, a. Below these rows is the statement G C F = 2 times 3 times a and the statement G C F = 6 a. Below this is the expression negative 6 a 2 plus 36 a. Then each term is factored negative 6 a times a minus negative 6 a times 6. The factored expression is written negative 6 a times (a minus 6). Under this the expression negative 6 a(a minus 6) is multiplied to check. The product is negative 6 a 2 plus 36 a.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\">Since the leading coefficient is negative, the GCF is negative, \u22126<em data-effect=\"italics\">a<\/em>.<\/td>\n<td><span id=\"eip-id1172183451295\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\n<span id=\"fs-id1167267738277\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term using the GCF.<\/td>\n<td><span id=\"eip-id1172183411347\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172183411364\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(-6a\\left(a-6\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(-6a\\cdot a+\\left(-6a\\right)\\left(-6\\right)\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\\(-6{a}^{2}+36a\\checkmark\\)<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345451505\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345451508\" data-type=\"exercise\">\n<div id=\"fs-id1168342104232\" data-type=\"problem\">\n<p id=\"fs-id1168342104234\">Factor: \\(-4{b}^{2}+16b\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345530191\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345530193\">\\(-4b\\left(b-4\\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 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345578926\" data-type=\"problem\">\n<p id=\"fs-id1168345578928\">Factor: \\(-7{a}^{2}+21a\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341861254\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168341861256\">\\(-7a\\left(a-3\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342180636\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345578924\" data-type=\"exercise\">\n<div id=\"fs-id1168341861254\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345414772\" data-type=\"problem\">\n<p id=\"fs-id1168345414774\">Factor: \\(5q\\left(q+7\\right)-6\\left(q+7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341906548\" 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-id1168345423614\">The GCF is the binomial \\(q+7\\).<\/p>\n\n<table id=\"fs-id1167271086070\" class=\"grid\" summary=\"This figure has the steps to factor 5 q times (q plus 7) minus 6 times (q plus 7). The first row has the expression 5 q times (q plus 7) minus 6 times (q plus 7) with the (q plus 7) factors labeled as the G C F. Then, the complete factoring, (q + 7) times (5 q minus 6). Check on your own by multiplying.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 330.938px;\"><\/td>\n<td style=\"width: 225.483px;\"><span id=\"fs-id1167270994367\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 330.938px;\">Factor the GCF, (<em data-effect=\"italics\">q<\/em> + 7).<\/td>\n<td style=\"width: 225.483px;\"><span id=\"fs-id1167271010385\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 330.938px;\">Check on your own by multiplying.<\/td>\n<td style=\"width: 225.483px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342180734\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345724061\" data-type=\"exercise\">\n<div id=\"fs-id1168345724063\" data-type=\"problem\">\n<p id=\"fs-id1168345724065\">Factor: \\(4m\\left(m+3\\right)-7\\left(m+3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345543440\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1168345543442\">\\(\\left(m+3\\right)\\left(4m-7\\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 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345521993\" data-type=\"problem\">\n<p id=\"fs-id1168345521995\">Factor: \\(8n\\left(n-4\\right)+5\\left(n-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345439500\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345439502\">\\(\\left(n-4\\right)\\left(8n+5\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Factor by Grouping<\/h1>\n<p id=\"fs-id1168345688046\">When there is no common factor of all the terms of a polynomial, look for a common factor in just some of the terms. When there are four terms, a good way to start is by separating the polynomial into two parts with two terms in each part. Then look for the GCF in each part. If the polynomial can be factored, you will find a common factor emerges from both parts.<\/p>\n<p id=\"fs-id1168345423454\">(Not all polynomials can be factored. Just like some numbers are prime, some polynomials are prime.)<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Factor by Grouping<\/div>\n<div id=\"fs-id1168345423460\" data-type=\"exercise\">\n<div id=\"fs-id1168341915998\" data-type=\"problem\">\n<p id=\"fs-id1168341916003\">Factor: \\(xy+3y+2x+6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345386334\" 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-id1168345439520\" data-type=\"media\" data-alt=\"This table gives the steps for factoring x y + 3 y + 2 x + 6. In the first row there is the statement, \u201cgroup terms with common factors\u201d. In the next column, there is the statement of no common factors of all 4 terms. The last column shows the first two terms grouped and the last two terms grouped.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015a_img_new.jpg\" alt=\"This table gives the steps for factoring x y + 3 y + 2 x + 6. In the first row there is the statement, \u201cgroup terms with common factors\u201d. In the next column, there is the statement of no common factors of all 4 terms. The last column shows the first two terms grouped and the last two terms grouped.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345517636\" data-type=\"media\" data-alt=\"The second row has the statement, \u201cfactor out the common factor from each group\u201d. The second column in the second row states to factor out the GCF from the two separate groups. The third column in the second row has the expression y(x + 3) + 2(x + 3).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015b_img_new.jpg\" alt=\"The second row has the statement, \u201cfactor out the common factor from each group\u201d. The second column in the second row states to factor out the GCF from the two separate groups. The third column in the second row has the expression y(x + 3) + 2(x + 3).\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168345668202\" data-type=\"media\" data-alt=\"The third row has the statement, \u201cfactor the common factor from the expression\u201d. The second column in this row points out there is a common factor of (x + 3). The third column in the third row shows the factor of (x + 3) factored from the two groups, (x + 3) times (y + 2).\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015c_img_new.jpg\" alt=\"The third row has the statement, \u201cfactor the common factor from the expression\u201d. The second column in this row points out there is a common factor of (x + 3). The third column in the third row shows the factor of (x + 3) factored from the two groups, (x + 3) times (y + 2).\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1168341917603\" data-type=\"media\" data-alt=\"The last row has the statement, \u201ccheck\u201d. The second column in this row states to multiply (x + 3)(y + 2). The product is shown in the last column of the original polynomial x y + 3 y + 2 x + 6.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015d_img_new.jpg\" alt=\"The last row has the statement, \u201ccheck\u201d. The second column in this row states to multiply (x + 3)(y + 2). The product is shown in the last column of the original polynomial x y + 3 y + 2 x + 6.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345487406\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171632\" data-type=\"exercise\">\n<div id=\"fs-id1168342171634\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345487406\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171632\" data-type=\"exercise\">\n<div id=\"fs-id1168342171634\" data-type=\"problem\">\n<p id=\"fs-id1168342171636\">Factor: \\(xy+8y+3x+24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168341923798\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168341923800\">\\(\\left(x+8\\right)\\left(y+3\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345745008\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345745011\" data-type=\"exercise\">\n<div id=\"fs-id1168345486734\" data-type=\"problem\"><\/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 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345486734\" data-type=\"problem\">\n<p id=\"fs-id1168345486736\">Factor: \\(ab+7b+8a+56\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345466322\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345708214\">\\(\\left(a+7\\right)\\left(b+8\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\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\nFactor by grouping.\n<ol>\n \t<li>Group terms with common factors.<\/li>\n \t<li>Factor out the common factor in each group.<\/li>\n \t<li>Factor the common factor from the expression.<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341852746\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341962937\" data-type=\"problem\">\n<p id=\"fs-id1168341962939\">Factor: \\({x}^{2}+3x-2x-6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345424536\" data-type=\"solution\">\n<div data-type=\"title\">\n\n<strong>Solution<\/strong>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">There is no GCF in all four terms.<\/td>\n<td style=\"width: 50%;\">\\({x}^{2}+3x-2x-6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Separate into two parts.<\/td>\n<td style=\"width: 50%;\">\\(\\underbrace{{x}^{2}+3x}\\underbrace{-2x-6}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms.<\/td>\n<td style=\"width: 50%;\">\\(\\begin{array}{c}x\\left(x+3\\right)-2\\left(x+3\\right)\\\\\u00a0 \\left(x+3\\right)\\left(x-2\\right)\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Check on your own by multiplying.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345466016\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341906472\" data-type=\"exercise\">\n<div id=\"fs-id1168341906474\" data-type=\"problem\">\n<p id=\"fs-id1168341906476\">Factor: \\({x}^{2}+2x-5x-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345661386\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345661388\">\\(\\left(x-5\\right)\\left(x+2\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345630365\" class=\"media-2\" data-type=\"note\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342171747\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171751\" data-type=\"exercise\">\n<div id=\"fs-id1168345385682\" data-type=\"problem\">\n<p id=\"fs-id1168345385684\">Factor: \\({y}^{2}+4y-7y-28\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1168345558127\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1168345558129\">\\(\\left(y+4\\right)\\left(y-7\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345630368\">Access these online resources for additional instruction and practice with greatest common factors (GFCs) and factoring by grouping.<\/p>\n\n<ul id=\"fs-id1168345386819\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/25GCF1\">Greatest Common Factor (GCF)<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25GCF2\">Factoring Out the GCF of a Binomial<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25GCF3\">Greatest Common Factor (GCF) of Polynomials<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1168345558554\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Finding the Greatest Common Factor (GCF):<\/strong> To find the GCF of two expressions:\n<ol id=\"fs-id1168745400837\" class=\"stepwise\" type=\"1\">\n \t<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n \t<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n \t<li>Bring down the common factors that all expressions share.<\/li>\n \t<li>Multiply the factors.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">Factor the Greatest Common Factor from a Polynomial:<\/strong> To factor a greatest common factor from a polynomial:\n<ol id=\"fs-id1168741805522\" class=\"stepwise\" type=\"1\">\n \t<li>Find the GCF of all the terms of the polynomial.<\/li>\n \t<li>Rewrite each term as a product using the GCF.<\/li>\n \t<li>Use the \u2018reverse\u2019 Distributive Property to factor the expression.<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">Factor by Grouping:<\/strong> To factor a polynomial with 4 four or more terms\n<ol id=\"fs-id1168745075740\" class=\"stepwise\" type=\"1\">\n \t<li>Group terms with common factors.<\/li>\n \t<li>Factor out the common factor in each group.<\/li>\n \t<li>Factor the common factor from the expression.<\/li>\n \t<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1168345539526\">\n \t<dt>factoring<\/dt>\n \t<dd id=\"fs-id1168345539531\">Factoring is splitting a product into factors; in other words, it is the reverse process of multiplying.<\/dd>\n<\/dl>\n<dl id=\"fs-id1168345448206\">\n \t<dt>greatest common factor<\/dt>\n \t<dd id=\"fs-id1168345448211\">The greatest common factor is the largest expression that is a factor of two or more expressions is the greatest common factor (GCF).<\/dd>\n<\/dl>\nType your textbox content here.\n\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Find the Greatest Common Factor of Two or More Expressions<\/h2>\n<p id=\"fs-id1168741931620\">In the following exercises, find the greatest common factor.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 126px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">1. 8, 18<\/td>\n<td style=\"width: 50%; height: 14px;\">2. 24, 40<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">3. 72, 162<\/td>\n<td style=\"width: 50%; height: 14px;\">4. 150, 275<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">5. 10<em data-effect=\"italics\">a<\/em>, 50<\/td>\n<td style=\"width: 50%; height: 14px;\">6. 5<em data-effect=\"italics\">b<\/em>, 30<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">7. \\(3x,10{x}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">8. \\(21{b}^{2},14b\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">9. \\(8{w}^{2},24{w}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">10. \\(30{x}^{2},18{x}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">11. \\(10{p}^{3}q,12p{q}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">12. \\(8{a}^{2}{b}^{3},10a{b}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">13. \\(12{m}^{2}{n}^{3},30{m}^{5}{n}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">14. \\(28{x}^{2}{y}^{4},42{x}^{4}{y}^{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">15. \\(10{a}^{3},12{a}^{2},14a\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">16. \\(20{y}^{3},28{y}^{2},40y\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">17. \\(35{x}^{3},10{x}^{4},5{x}^{5}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">18. \\(27{p}^{2},45{p}^{3},9{p}^{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Factor the Greatest Common Factor from a Polynomial<\/h2>\n<p id=\"fs-id1168745121996\">In the following exercises, factor the greatest common factor from each polynomial.<\/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;\">19. \\(4x+20\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">20. \\(8y+16\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">21. \\(6m+9\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">22. \\(14p+35\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">23. \\(9q+9\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">24. \\(7r+7\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. \\(8m-8\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">26. \\(4n-4\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. \\(9n-63\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">28. \\(45b-18\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. \\(3{x}^{2}+6x-9\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">30. \\(4{y}^{2}+8y-4\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. \\(8{p}^{2}+4p+2\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">32. \\(10{q}^{2}+14q+20\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. \\(8{y}^{3}+16{y}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">34. \\(12{x}^{3}-10x\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. \\(5{x}^{3}-15{x}^{2}+20x\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">36. \\(8{m}^{2}-40m+16\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. \\(12x{y}^{2}+18{x}^{2}{y}^{2}-30{y}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">38. \\(21p{q}^{2}+35{p}^{2}{q}^{2}-28{q}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. \\(-2x-4\\)<\/td>\n<td style=\"width: 50%;\">40 \\(-3b+12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. \\(5x\\left(x+1\\right)+3\\left(x+1\\right)\\)<\/td>\n<td style=\"width: 50%;\">42. \\(2x\\left(x-1\\right)+9\\left(x-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. \\(3b\\left(b-2\\right)-13\\left(b-2\\right)\\)<\/td>\n<td style=\"width: 50%;\">44. \\(6m\\left(m-5\\right)-7\\left(m-5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Factor by Grouping<\/h2>\n<p id=\"fs-id1168745400658\">In the following exercises, factor by grouping.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">45. \\(xy+2y+3x+6\\)<\/td>\n<td style=\"width: 50%;\">46. \\(mn+4n+6m+24\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. \\(uv-9u+2v-18\\)<\/td>\n<td style=\"width: 50%;\">48. \\(pq-10p+8q-80\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. \\({b}^{2}+5b-4b-20\\)<\/td>\n<td style=\"width: 50%;\">50. \\({m}^{2}+6m-12m-72\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">51. \\({p}^{2}+4p-9p-36\\)<\/td>\n<td style=\"width: 50%;\">52. \\({x}^{2}+5x-3x-15\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Mixed Practice<\/h2>\n<p id=\"fs-id1168741893632\">In the following exercises, factor.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">53. \\(-20x-10\\)<\/td>\n<td style=\"width: 50%;\">54. \\(5{x}^{3}-{x}^{2}+x\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">55. \\(3{x}^{3}-7{x}^{2}+6x-14\\)<\/td>\n<td style=\"width: 50%;\">56. \\({x}^{3}+{x}^{2}-x-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">57. \\({x}^{2}+xy+5x+5y\\)<\/td>\n<td style=\"width: 50%;\">58. \\(5{x}^{3}-3{x}^{2}-5x-3\\)<\/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%;\">59.<strong data-effect=\"bold\"> Area of a rectangle<\/strong> The area of a rectangle with length 6 less than the width is given by the expression \\({w}^{2}-6w\\), where \\(w=\\) width. Factor the greatest common factor from the polynomial.<\/td>\n<td style=\"width: 50%;\">60. <strong data-effect=\"bold\">Height of a baseball<\/strong> The height of a baseball <em data-effect=\"italics\">t<\/em> seconds after it is hit is given by the expression \\(-16{t}^{2}+80t+4\\). Factor the greatest common factor from the polynomial.<\/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%;\">61. The greatest common factor of 36 and 60 is 12. Explain what this means.<\/td>\n<td style=\"width: 50%;\">62. What is the GCF of \\({y}^{4},{y}^{5}\\), and \\({y}^{10}\\)? Write a general rule that tells you how to find the GCF of \\({y}^{a},{y}^{b}\\), and \\({y}^{c}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 192px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">1. 2<\/td>\n<td style=\"width: 50%; height: 16px;\">3. 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">5. 10<\/td>\n<td style=\"width: 50%; height: 16px;\">7. \\(x\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">9. \\(8{w}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">11. \\(2pq\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">13. \\(6{m}^{2}{n}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">15. \\(2a\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">17. \\(5{x}^{3}\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">19. \\(4\\left(x+5\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">21. \\(3\\left(2m+3\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">23. \\(9\\left(q+1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">25. \\(8\\left(m-1\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">27. \\(9\\left(n-7\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">29. \\(3\\left({x}^{2}+2x-3\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">31. \\(2\\left(4{p}^{2}+2p+1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">33. \\(8{y}^{2}\\left(y+2\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">35. \\(5x\\left({x}^{2}-3x+4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">37. \\(6{y}^{2}\\left(2x+3{x}^{2}-5y\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">39. \\(-2\\left(x+4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">41. \\(\\left(x+1\\right)\\left(5x+3\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">43. \\(\\left(b-2\\right)\\left(3b-13\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">45. \\(\\left(y+3\\right)\\left(x+2\\right)\\)<\/td>\n<td style=\"width: 50%; height: 16px;\">47. \\(\\left(u+2\\right)\\left(v-9\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. \\(\\left(b-4\\right)\\left(b+5\\right)\\)<\/td>\n<td style=\"width: 50%;\">51. \\(\\left(p-9\\right)\\left(p+4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. \\(-10\\left(2x+1\\right)\\)<\/td>\n<td style=\"width: 50%;\">55. \\(\\left({x}^{2}+2\\right)\\left(3x-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">57. \\(\\left(x+y\\right)\\left(x+5\\right)\\)<\/td>\n<td style=\"width: 50%;\">59. \\(w\\left(w-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61.\u00a0Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cGreatest Common Factor and Factor by Grouping\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.<!-- pb_fixme -->","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>Find the greatest common factor of two or more expressions<\/li>\n<li>Factor the greatest common factor from a polynomial<\/li>\n<li>Factor by grouping<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Find the Greatest Common Factor of Two or More Expressions<\/h1>\n<p id=\"fs-id1168345388781\">Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring.<\/p>\n<p><span id=\"fs-id1168345656426\" data-type=\"media\" data-alt=\"This figure has two factors being multiplied. They are 8 and 7. Beside this equation there are other factors multiplied. They are 2x and (x+3). The product is given as 2x^2 plus 6x. Above the figure is an arrow towards the right with multiply inside. Below the figure is an arrow to the left with factor inside.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_Elem20Alg_Figure_07_01_001_img_new.jpg\" alt=\"This figure has two factors being multiplied. They are 8 and 7. Beside this equation there are other factors multiplied. They are 2x and (x+3). The product is given as 2x^2 plus 6x. Above the figure is an arrow towards the right with multiply inside. Below the figure is an arrow to the left with factor inside.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1168345677793\">We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the greatest common factor of two or more expressions. The method we use is similar to what we used to find the LCM.<\/p>\n<div id=\"fs-id1168345291091\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Greatest Common Factor<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The <span class=\"no-emphasis\" data-type=\"term\">greatest common factor<\/span> (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168342171304\">First we\u2019ll find the GCF of two numbers.<\/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 Find the Greatest Common Factor of Two or More Expressions<\/div>\n<div id=\"fs-id1168345255994\" data-type=\"exercise\">\n<div id=\"fs-id1168345192684\" data-type=\"problem\">\n<p id=\"fs-id1168341973334\">Find the GCF of 54 and 36<\/p>\n<\/div>\n<div id=\"fs-id1168345424484\" 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-id1168345635362\" data-type=\"media\" data-alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, factor each coefficient into primes and write all variables with exponents in expanded form. The second column in the first row has \u201cfactor 54 and 36\u201d. The third column in the first row has 54 and 36 factored with factor trees. The prime factors of 54 are circled and are 3, 3, 2, and3. The prime factors of 36 are circled and are 2,3,2,3.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002a_img_new.jpg\" alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, factor each coefficient into primes and write all variables with exponents in expanded form. The second column in the first row has \u201cfactor 54 and 36\u201d. The third column in the first row has 54 and 36 factored with factor trees. The prime factors of 54 are circled and are 3, 3, 2, and3. The prime factors of 36 are circled and are 2,3,2,3.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345342690\" data-type=\"media\" data-alt=\"The second row has the second step of \u201cin each column, circle the common factors. The second column in the second row has the statement \u201ccircle the 2, 3 and 3 that are shared by both numbers\u201d. The third column in the second row has the prime factors of 36 and 54 in rows above each other. The common factors of 2, 3, and 3 are circled.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002b_img_new.jpg\" alt=\"The second row has the second step of \u201cin each column, circle the common factors. The second column in the second row has the statement \u201ccircle the 2, 3 and 3 that are shared by both numbers\u201d. The third column in the second row has the prime factors of 36 and 54 in rows above each other. The common factors of 2, 3, and 3 are circled.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345425779\" data-type=\"media\" data-alt=\"The third row has the step \u201cbring down the common factors that all expressions share\u201d. The second column in the third row has \u201cbring down the 2,3, and 3 then multiply\u201d. The third column in the third row has \u201cGCF = 2 times 3 times 3\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002c_img_new.jpg\" alt=\"The third row has the step \u201cbring down the common factors that all expressions share\u201d. The second column in the third row has \u201cbring down the 2,3, and 3 then multiply\u201d. The third column in the third row has \u201cGCF = 2 times 3 times 3\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345434590\" data-type=\"media\" data-alt=\"The fourth row has the fourth step \u201cmultiply the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has \u201cGCF = 18\u201d and \u201cthe GCF of 54 and 36 is 18\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_002d_img_new.jpg\" alt=\"The fourth row has the fourth step \u201cmultiply the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has \u201cGCF = 18\u201d and \u201cthe GCF of 54 and 36 is 18\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1168345633976\">Notice that, because the GCF is a factor of both numbers, 54 and 36 can be written as multiples of 18<\/p>\n<div id=\"fs-id1168745570074\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-525122608af8e07fb8c84f371535bb53_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;&#53;&#52;&#61;&#49;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#92;&#32;&#51;&#54;&#61;&#49;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"81\" style=\"vertical-align: -11px;\" \/><\/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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341907611\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345670292\" data-type=\"exercise\">\n<div id=\"fs-id1168345743063\" data-type=\"problem\">\n<p id=\"fs-id1168345329454\">Find the GCF of 48 and 80.<\/p>\n<\/div>\n<div id=\"fs-id1168341916032\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345251014\">16<\/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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345522058\" data-type=\"problem\">\n<p id=\"fs-id1168345300785\">Find the GCF of 18 and 40.<\/p>\n<\/div>\n<div id=\"fs-id1168345450073\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345509731\">2<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345487595\">We summarize the steps we use to find the GCF below.<\/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>Find the Greatest Common Factor (GCF) of two expressions<\/p>\n<ol id=\"fs-id1168741892867\" class=\"stepwise\" type=\"1\">\n<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n<li>Bring down the common factors that all expressions share.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>In the first example, the GCF was a constant. In the next two examples, we will get variables in the greatest common factor.<\/p>\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-id1168345647941\" data-type=\"problem\">\n<p id=\"fs-id1168345227453\">Find the greatest common factor of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-418dfc501d1719914298db26f7c825ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5437fd785e048ca00b777c3135f25ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345557943\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172184762201\" class=\"unnumbered unstyled\" summary=\"This image has two terms above each other with the factors to the right. The first term is 27 x three times and has factors 3, 3, 3, x, x, x. The second term is 18 x 4 times and has factors 2, 3, 3, x, x, x, x. Below these two rows is a line. Below the line are the two statements \u201cGCF = 3 times 3 times x times x times x\u201d and \u201cG C F = 9 x 3 times\u201d. Below this is the statement \u201cthe G C F of 27 x 3 times and 18 x 4 times is 9 x 3 times\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td><span id=\"eip-id1172184762222\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Bring down the common factors.<\/td>\n<td><span id=\"eip-id1172184770130\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply the factors.<\/td>\n<td><span id=\"eip-id1172184770147\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-418dfc501d1719914298db26f7c825ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5437fd785e048ca00b777c3135f25ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c6975da599e97c962b1fc9a4e1e1192_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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<div id=\"fs-id1168345622514\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345367998\" data-type=\"exercise\">\n<div id=\"fs-id1168345240940\" data-type=\"problem\">\n<p id=\"fs-id1168345363065\">Find the GCF: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d4fe2c37bef5a098922f235b0b187fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345191223\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345414926\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9608403b176cb023606ca01493d9f883_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/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-id1168345357691\" data-type=\"problem\">\n<p id=\"fs-id1168345445832\">Find the GCF: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84564446dc0278b1b0ee46621bd3b046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#50;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345442278\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168341840802\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-649c835f6f65cf7f7c974a270b0c159b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341973453\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345578746\" data-type=\"exercise\">\n<div id=\"fs-id1168345442278\" data-type=\"solution\">\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-id1168345646517\" data-type=\"problem\">\n<p id=\"fs-id1168345195586\">Find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6589997f0e635a47a8a5215be2fbe1d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#44;&#54;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345689915\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187711032\" class=\"unnumbered unstyled can-break\" style=\"height: 123px;\" summary=\"This image has two terms above each other with the factors to the right. The first term is 4 x squared times y and has factors 2, 2, x, x, y. The second term is 6 times x times y cubed and has factors 2, 3, x, y, y, y. Below these two rows is a line. Below the line are two statements \u201cG C F = 2 times x times y\u201d and \u201cG C F = 2 x y\u201d. Below this is the statement \u201cthe G C F of 4 times x squared times y and 6 times x times y cubed is 2 x y\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 73px;\">\n<td style=\"height: 73px; width: 826.406px;\">Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td style=\"height: 73px; width: 404.406px;\"><span id=\"eip-id1172188156282\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 826.406px;\">Bring down the common factors.<\/td>\n<td style=\"height: 18px; width: 404.406px;\"><span id=\"eip-id1172188156299\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 826.406px;\">Multiply the factors.<\/td>\n<td style=\"height: 18px; width: 404.406px;\"><span id=\"eip-id1172188156316\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_016c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 826.406px;\"><\/td>\n<td style=\"height: 14px; width: 404.406px;\">The GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baec132ab75214c440bbd16127f5715f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46b4c15e556e197c239aac25eef65137_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc6cc9989df175379a312b0b2ee994f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#120;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: -3px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345434578\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345357736\" data-type=\"exercise\">\n<div id=\"fs-id1168345742331\" data-type=\"problem\">\n<p id=\"fs-id1168345230263\">Find the GCF: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-256d8ee0d723865074b14e661fb0e196_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#97;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#44;&#56;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345420190\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345377018\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ddef4007f116e84febe922aa24a12bca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/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-id1168345677485\" data-type=\"problem\">\n<p id=\"fs-id1168345262355\">Find the GCF: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dfa9cddded57c6d7fd9e8835e7044ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345415642\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345553226\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a57c6258c9ae266ab047465ecfa5a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345426967\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345370552\" data-type=\"exercise\">\n<div id=\"fs-id1168345415642\" data-type=\"solution\">\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-id1168345292398\" data-type=\"problem\">\n<p id=\"fs-id1168345644039\">Find the GCF of: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1ba121894699f6b095e1222ddebde58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345675934\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172185570976\" class=\"unnumbered unstyled\" style=\"height: 151px;\" summary=\"This image has three terms above each other with the factors to the right. The first term is 21 x three times and has factors 3,7, x, x, x. The second term is 9 x 2 times and has factors 3, 3, x, x. The third term is 15 x and has factors 3, 5, x. Below these three rows is a line. Below the line are the two statements \u201cG C F = 3 times x\u201d and \u201cG C F = 3 times x\u201d. Below this is the statement \u201cthe G C F of 21 x 3 times, 9 x 2 times, and 15 x is 3 x\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 109px;\">\n<td style=\"height: 109px; width: 826.406px;\">Factor each coefficient into primes and write the variables with exponents in expanded form. Circle the common factors in each column.<\/td>\n<td style=\"height: 109px; width: 372.406px;\"><span id=\"eip-id1172185570997\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 826.406px;\">Bring down the common factors.<\/td>\n<td style=\"height: 15px; width: 372.406px;\"><span id=\"eip-id1172185571014\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 13px;\">\n<td style=\"height: 13px; width: 826.406px;\">Multiply the factors.<\/td>\n<td style=\"height: 13px; width: 372.406px;\"><span id=\"eip-id1172185571030\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 826.406px;\"><\/td>\n<td style=\"height: 14px; width: 372.406px;\">The GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fd6c3f6114fa33cb3d4f11ed2cbdbde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1b5fd89b5219b9297f899b52acb9e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15280d18608293c164f1ad95092a47c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"27\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345565463\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345217896\" data-type=\"exercise\">\n<div id=\"fs-id1168345194498\" data-type=\"problem\">\n<p id=\"fs-id1168345743857\">Find the greatest common factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fddb81b40737fa60877cee417a3a5f96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#44;&#51;&#53;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#44;&#50;&#48;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345511096\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345635282\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73d70cc15de8dab880a6427ad70ed4f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345451904\" data-type=\"problem\">\n<p id=\"fs-id1168345228410\">Find the greatest common factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59a26ae5b7c636519d032c870ee2e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#55;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#48;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345671388\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345425124\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21c22354b95d8047439895fca18899e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor the Greatest Common Factor from a Polynomial<\/h1>\n<p id=\"fs-id1168345261365\">Just like in arithmetic, where it is sometimes useful to represent a number in factored form (for example, 12 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c71ad2d3e43a4c1dd2e8bc8695f7b12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d03c93c676d6a0b5eea791329cc3c0b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/>, in algebra, it can be useful to represent a polynomial in factored form. One way to do this is by finding the GCF of all the terms. Remember, we multiply a polynomial by a monomial as follows:<\/p>\n<div id=\"fs-id1168345251904\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92f4c3a08c261120022c927db8a1b1d9_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;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#125;&#92;&#92;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#32;&#38;&#32;&#92;&#92;&#32;&#50;&#120;&#43;&#49;&#52;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#114;&#111;&#100;&#117;&#99;&#116;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"196\" style=\"vertical-align: -26px;\" \/><\/div>\n<p id=\"fs-id1168345420818\">Now we will start with a product, like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff68c85253b6989ba53ee811852f64da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/>, and end with its factors, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-490467179dcd3edaf12b8b465a0916d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>. To do this we apply the Distributive Property \u201cin reverse.\u201d<\/p>\n<p id=\"fs-id1168345195281\">We state the Distributive Property here just as you saw it in earlier chapters and \u201cin reverse.\u201d<\/p>\n<div id=\"fs-id1168345744805\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Distributive Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168345274390\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58797fcd980ddcdad97f6b6f5260b5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/p>\n<div id=\"fs-id1168345230029\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4040089f7ef95940c581b0255da8a89_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;&#99;&#125;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#97;&#98;&#43;&#97;&#99;&#61;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"452\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345397940\">The form on the left is used to multiply. The form on the right is used to factor.<\/p>\n<\/div>\n<p id=\"fs-id1168345560598\">So how do you use the Distributive Property to factor a polynomial? You just find the GCF of all the terms and write the polynomial as a product!<\/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 data-type=\"title\">How to Factor the Greatest Common Factor from a Polynomial<\/div>\n<div id=\"fs-id1168345406988\" data-type=\"exercise\">\n<div id=\"fs-id1168341973830\" data-type=\"problem\">\n<p id=\"fs-id1168345675931\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2ddf3bf320f30ca9126b5781310e606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345429720\" 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-id1168345276045\" data-type=\"media\" data-alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, \u201cFind the G C F of all the terms of the polynomial\u201d. The second column in the first row has \u201cfind the G C F of 4 x and 12\u201d. The third column in the first row has 4 x factored as 2 times 2 times x and below it 18 factored as 2 times 2 times 3. Then, below the factors are the statements, \u201cG C F = 2 times 2\u201d and \u201cG C F = 4\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005a_img_new.jpg\" alt=\"This table has three columns. In the first column are the steps for factoring. The first row has the first step, \u201cFind the G C F of all the terms of the polynomial\u201d. The second column in the first row has \u201cfind the G C F of 4 x and 12\u201d. The third column in the first row has 4 x factored as 2 times 2 times x and below it 18 factored as 2 times 2 times 3. Then, below the factors are the statements, \u201cG C F = 2 times 2\u201d and \u201cG C F = 4\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345347355\" data-type=\"media\" data-alt=\"The second row has the second step \u201crewrite each term as a product using the G C F\u201d. The second column in the second row has the statement \u201cRewrite 4 x and 12 as products of their G C F, 4\u201d Then the two equations 4 x = 4 times x and 12 = 4 times 3. The third column in the second row has the expressions 4x + 12 and below this 4 times x + 4 times 3.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005b_img_new.jpg\" alt=\"The second row has the second step \u201crewrite each term as a product using the G C F\u201d. The second column in the second row has the statement \u201cRewrite 4 x and 12 as products of their G C F, 4\u201d Then the two equations 4 x = 4 times x and 12 = 4 times 3. The third column in the second row has the expressions 4x + 12 and below this 4 times x + 4 times 3.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345270344\" data-type=\"media\" data-alt=\"The third row has the step \u201cUse the reverse distributive property to factor the expression\u201d. The second column in the third row is blank. The third column in the third row has \u201c4(x + 3)\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005c_img_new.jpg\" alt=\"The third row has the step \u201cUse the reverse distributive property to factor the expression\u201d. The second column in the third row is blank. The third column in the third row has \u201c4(x + 3)\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345432733\" data-type=\"media\" data-alt=\"The fourth row has the fourth step \u201ccheck by multiplying the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has three expressions. The first is 4(x + 3), the second is 4 times x + 4 times 3. The third is 4 x + 12.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_005d_img_new.jpg\" alt=\"The fourth row has the fourth step \u201ccheck by multiplying the factors\u201d. The second column in the fourth row is blank. The third column in the fourth row has three expressions. The first is 4(x + 3), the second is 4 times x + 4 times 3. The third is 4 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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345276005\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345688289\" data-type=\"exercise\">\n<div id=\"fs-id1168345300927\" data-type=\"problem\">\n<p id=\"fs-id1168345465917\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb754b7a54fa0e92512ab03221e57d82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#97;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345357504\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345228984\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81bfcfa6b9d00bf07ac3d407eee8bca3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" 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-id1168345500408\" data-type=\"problem\">\n<p id=\"fs-id1168345251303\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b9f1b25986a6c867216a166c2a2df85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#98;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345192702\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345219462\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8df60a3f26b603f8c8cd5eb0690dad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\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<p>Factor the greatest common factor from a polynomial.<\/p>\n<ol>\n<li>Find the GCF of all the terms of the polynomial.<\/li>\n<li>Rewrite each term as a product using the GCF.<\/li>\n<li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345448814\" data-type=\"note\">\n<div data-type=\"title\">Factor as a Noun and a Verb<\/div>\n<p id=\"fs-id1168341907170\">We use \u201cfactor\u201d as both a noun and a verb.<\/p>\n<p><span id=\"fs-id1168345508580\" data-type=\"media\" data-alt=\"This figure has two statements. The first statement has \u201cnoun\u201d. Beside it the statement \u201c7 is a factor of 14\u201d labeling the word factor as the noun. The second statement has \u201cverb\u201d. Beside this statement is \u201cfactor 3 from 3a + 3 labeling factor as the verb.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_017_img_new.jpg\" alt=\"This figure has two statements. The first statement has \u201cnoun\u201d. Beside it the statement \u201c7 is a factor of 14\u201d labeling the word factor as the noun. The second statement has \u201cverb\u201d. Beside this statement is \u201cfactor 3 from 3a + 3 labeling factor as the verb.\" data-media-type=\"image\/jpeg\" \/><\/span><\/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-id1168341862477\" data-type=\"problem\">\n<p id=\"fs-id1168345434116\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19c30164a31e4da068c6552af22a03c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345292167\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172185559033\" class=\"unnumbered unstyled\" summary=\"This figure has the steps for factoring 5a + 5. First, is finding the G C F of 5 a and 5. The first row has the equation 5 a equals 5 times a. Below this there is the equation 5 equals 5. In these two equations, the 5\u2019s are circled on the right hand side. Below these equations is the statement, G C F equals 5. Below this is the expression 5 a + 5. Below this, the terms of the expression are written with factors, 5 times a + 5 times 1. Below this is the expression 5(a + 1), showing the 5 factored from the expression. Below this, the factoring is checked by multiplying 5(a + 1). The step below this is 5 times a + 5 times 1. Then, the answer, 5a + 5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of 5<em data-effect=\"italics\">a<\/em> and 5.<\/td>\n<td><span id=\"eip-id1172185559054\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172185559069\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172186035559\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the Distributive Property &#8220;in reverse&#8221; to factor the GCF.<\/td>\n<td><span id=\"eip-id1172186035575\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying the factors to get the orginal polynomial.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b21e6488d875a0d9ffbf07c3a854970c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0976e52c7a6e5d99723a1dcc8b35a545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#43;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6495f1268b059a01a104c4ce241d9375_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#97;&#43;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345436261\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345665214\" data-type=\"exercise\">\n<div id=\"fs-id1168345216274\" data-type=\"problem\">\n<p id=\"fs-id1168345550230\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5cac2d97284c034d40ceae59ad9eb3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#120;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345427982\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345726539\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-760ef3b09fb075752861ce1711721bfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345517802\" data-type=\"problem\">\n<p id=\"fs-id1168345216876\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c31614a2bb0d203f7a8fa7fce1399227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#112;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345423512\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168341962889\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60e9713244e95e2f9ee554fe0c388006_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345448711\">The expressions in the next example have several factors in common. Remember to write the GCF as the product of all the common factors.<\/p>\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-id1168341864057\" data-type=\"problem\">\n<p id=\"fs-id1168345507877\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dcf05ff81175f366096fa5cdd819398b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345202847\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172183494582\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for factoring 12 x minus 60. First, is finding the GCF of 12 x and 60. Two equations are written. The first equation has the factors of 12 x = 2 times 2 times 3 times x. Below this, the equation 60 = 2 times 2 times 3 times 5. In these equations the common factors of 2, 2, and 3 are circled. Below these two equations is are the statements G C F = 2 times 2 times 3 and G C F = 12. Then, the expression 12 x minus 60 is written. Below is the expression with 12 factored from both terms, 12 times x minus 12 times 5. Then, the factoring is written 12 times x \u2013minus 5, with x minus 5 in parentheses. Finally, the factoring is checked with multiplying 12 times x minus 5, x minus 5 in parentheses. The statement, 12 times x minus 12 times 5. Below this is the product 12 x minus 60.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of 12<em data-effect=\"italics\">x<\/em> and 60.<\/td>\n<td><span id=\"eip-id1172183494602\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172183494617\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172188156364\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172188156380\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying the factors.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cfdabb80dbc40925d427126c99cca296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c7d692f6e37289bc22b2df2bcc4db57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#45;&#49;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"100\" style=\"vertical-align: -1px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-98689f727a5851fb05ca0f383b55c12a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#45;&#54;&#48;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"81\" style=\"vertical-align: -1px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345723945\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345557216\" data-type=\"exercise\">\n<div id=\"fs-id1168345442218\" data-type=\"problem\">\n<p id=\"fs-id1168345302689\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5afcd1984770214553209f617b61e169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#117;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345466169\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168342170087\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-432a6186b4ab8f1d3eb0aebc9c1b903e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" 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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345269905\" data-type=\"problem\">\n<p id=\"fs-id1168345621361\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a90efd67f6e6c70781fec16757acb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#121;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"67\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168342048497\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345398080\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9272b15947cbfab5fac022a8cf9b4c49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345450727\">Now we\u2019ll factor the greatest common factor from a trinomial. We start by finding the GCF of all three terms.<\/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-id1168345530229\" data-type=\"problem\">\n<p id=\"fs-id1168345483991\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b4751e9ae719ed99b3f4b90d0cc89b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#52;&#121;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345574716\" 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-id1168345429115\">We start by finding the GCF of all three terms.<\/p>\n<table id=\"eip-id1172187652496\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for factoring 4 y squared plus 24 y plus 28. The first step is finding the G C F of 4 times y squared, 24 times y and 28. There are three equations written with factors. The first is 4 times y squared equals 2 times 2 times y times y. The second is 2 times 2 times 2 times 3 times y. The third is 2 times 2 times 7. In these equations the common factors of 2 and 2 are circled. Under these equations there is the statement G C F equals 2 times 2 and the statement G C F = 4. The next row has the polynomial 4 y squared plus 24 y plus 28. Under this, each term has the factor of 4, written 4 times y squared plus 4 times 6 y plus 4 times 7. The next expression has the 4 factored out, 4( y squared plus 6 y plus 7). Under this the factoring is checked by multiplying 4 (y squared plus 6 y plus7). The product is 4 times y squared + 24 y + 28.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27a6da6987a8c21eaa918b9915dc0b01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9030ca314dc08e0122c299eaf01859e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -4px;\" \/> and 28.<\/td>\n<td><span id=\"eip-id1172187652534\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187652549\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term as a product using the GCF.<\/td>\n<td><span id=\"eip-id1172187652566\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187652582\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check by mulitplying.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2aa05e83856551f94f61dd03a44ae861_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c87d2a56e546edaf6d2f936c7a5f842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#121;&#43;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9675b65a4ea84f5ad36bde3430da9e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#52;&#121;&#43;&#50;&#56;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345622986\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345508556\" data-type=\"exercise\">\n<div id=\"fs-id1168345508558\" data-type=\"problem\">\n<p id=\"fs-id1168345741313\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53c8e9ed7ef406cfae2ff1bc1165d3cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#53;&#120;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"115\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345398436\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345398438\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fdee68a63132bdbc2ec5b56a9e19f91e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -7px;\" \/><\/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-id1168345215798\" data-type=\"problem\">\n<p id=\"fs-id1168345677606\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7dc7c19e21f26a2424bc4309658d2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#121;&#43;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345418264\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345418266\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce94d40509daf6a6bcd9401230901365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#121;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345529877\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341861952\" data-type=\"exercise\">\n<div id=\"fs-id1168345418264\" 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-id1168341918996\" data-type=\"problem\">\n<p id=\"fs-id1168341918999\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b48f598a8d025a689b5f8f287329f631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"83\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168342169956\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187580327\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps for factoring 5 times x 3 times minus 25 x squared. First, is finding the G C F of 5 times x 3 times and 25 x squared. Two equations are written. The first equation has the factors of 5 times x 3 times equals 5 times x times x times x. Below this, the equation 25 times x squared equals 5 times 5 times x times x. In these equations the common factors of 5, x, and x are circled. Below these two equations is are the statements G C F = 5 times x times x and G C F = 5 x squared. Then, the expression 5 times x 3 times minus 25 x squared is written. Below is the expression with 5 times x squared factored from both terms, 5 x squared times x minus 5 x squared times 5. Then, the factoring is written 5 x squared times (x minus 5). Finally, the factoring is checked with multiplying 5 times x squared times (x minus 5). The statement, 5 x squared times x minus 5 x squared times 5. Below this is the product 5 x 3 \u2013 25 x 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ad8655a65bb986a62c563c119edd22c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07288c5e6c8d99d7a9ede77241ff58ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1172187218288\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187218304\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term.<\/td>\n<td><span id=\"eip-id1172187218320\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187218337\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae8f79497e72250d8a1f051bf8382915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e71575ea1d9ac9beb01a6a2812581a73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"119\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e29a2e49294f674bc0b707634091a7c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -1px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\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-id1168341901909\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341955830\" data-type=\"exercise\">\n<div id=\"fs-id1168341955832\" data-type=\"problem\">\n<p id=\"fs-id1168345419057\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7dd24d68b4a01395410c1e3dd28de1c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345461759\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345461762\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f116c86a7d534d4aa02e15978ff7a852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345638669\" data-type=\"problem\">\n<p id=\"fs-id1168345638672\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-818ffbe8cbe897deea153d42db2d9074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168342170077\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168342170079\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8aeab34fd2a80efaf7500d1ca3b2d964_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345530201\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345638667\" data-type=\"exercise\">\n<div id=\"fs-id1168342170077\" data-type=\"solution\">\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-id1168345542420\" data-type=\"problem\">\n<p id=\"fs-id1168345542422\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c9f9df1c39a521fb77e783ed7ba4a9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341962958\" 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-id1168341902398\">In a previous example we found the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1ba121894699f6b095e1222ddebde58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -4px;\" \/> to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<table id=\"eip-id1172187863365\" class=\"grid\" summary=\"This figure shows the steps to factoring 21 x 3 minus 9 x 2 +15 x. The G C F is given as 3 x. The first step writes the terms of the polynomial with 3 x factored from each, 3 x times 7 x 2 minus 3 x times 3 x + 3 x times 5. Then, the 3 x is factored for the answer, 3 x times (7 x 2 minus 3 x plus 5). Then, below the factored form the answer is checked by multiplying 3 x times (7 x 2 minus 3 x plus 5). Giving the product, 21 x 3 minus 9 x 2 plus 15 x.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172187863384\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term using the GCF, 3<em data-effect=\"italics\">x<\/em>.<\/td>\n<td><span id=\"eip-id1172187863401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172187863417\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f27948471534ef47e23678543e344d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc63912fbf63bb439e3b31b01cc514e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#120;&#43;&#51;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"192\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3cd88be74dfd665d72295fede3c2bc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"148\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345430922\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345434541\" data-type=\"exercise\">\n<div id=\"fs-id1168345434543\" data-type=\"problem\">\n<p id=\"fs-id1168345434545\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1baa3c2779f6a8d951cca457b43a0e69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"142\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341951011\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168341951013\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6544114854cddd4cb43439c1fa300ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"143\" style=\"vertical-align: -7px;\" \/><\/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-id1168345430714\" data-type=\"problem\">\n<p id=\"fs-id1168345430716\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f48d9fb45cfe2b31e6d1b95ee4415b69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345741381\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345741383\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3088f263861fef81bd9b0ecd96eabe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342170303\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342170306\" data-type=\"exercise\">\n<div id=\"fs-id1168345741381\" 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-id1168345669993\" data-type=\"problem\">\n<p id=\"fs-id1168345526582\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4514f8472d1b4835e15d749dd6a76b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;&#43;&#50;&#48;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"179\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341862559\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172186658692\" class=\"unnumbered unstyled can-break\" summary=\"This figure shows the steps to factor 8 m 3 minus 12 m 2 n plus 20 m n 2. First, the G C F of the terms 8 m 3, 12 m 2 n, and 20 m n 2 are found. These terms are written in rows factored. The rows are, 8 m 3 = 2 times 2 times 2 times m times m times m. The second row has 12 m 2 n = 2 times 2 times 3 times m times m times n. The third row is 20 m 2 n = 2 times 2 times 5 times m times n times n. The common factors of all three terms are circled, 2, 2, m. Below these rows is the statement G C F = 2 times 2 times m and the statement G C F = 4 m. Below this is the polynomial 8 m 3 minus 12 m 2 n plus 20 m n 2, then the terms with 4 m factored from each. 4 m times 2 m 2 minus 4 m times 3m n plus 4 m times 5 n 2. Below this is the factored polynomial 4 m times (2 m 2 minus 3m n plus 5 n 2). Then the factoring is checked by multiplying 4 m times (2 m 2 minus 3 m n plus 5 n 2), giving the product 8 m 3 minus 12 m 2 n plus 20 m n 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f82ab3de4b7660561c4507a1522dfe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe868f592e2bb59937afb98ab30679ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f240e8b81558515935992d15e5caedd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1172189038688\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1172189038704\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term.<\/td>\n<td><span id=\"eip-id1172187574020\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172189040472\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_011d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a84cf393e849236ffda32cbdfd904be7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#109;&#110;&#43;&#53;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"179\" style=\"vertical-align: -7px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-878715f657b3e89517917d3c575d884d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#109;&#110;&#43;&#52;&#109;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"249\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c749357eda32afb25a8c0086cc8159f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;&#43;&#50;&#48;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"193\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345560110\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345436546\" data-type=\"exercise\">\n<div id=\"fs-id1168345436548\" data-type=\"problem\">\n<p id=\"fs-id1168345530697\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5be9cb444d8900d66bfd8547780c7d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345540728\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345540730\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a25a496243908000580bad06246a8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#43;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -7px;\" \/><\/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 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345455411\" data-type=\"problem\">\n<p id=\"fs-id1168345455413\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2817d53f4e463d3924fc16d39a27eac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#57;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345409484\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345409486\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2547cb65a48a0bbe9971f1cf2cbcb98b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#112;&#113;&#43;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"146\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345522910\">When the leading coefficient is negative, we factor the negative out as part of the GCF.<\/p>\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-id1168345544292\" data-type=\"problem\">\n<p id=\"fs-id1168345544294\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe92824bf43c7f2f441187863a51eccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#121;&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345670114\" 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-id1168341890600\">When the leading coefficient is negative, the GCF will be negative.<\/p>\n<table id=\"eip-id1172187954751\" class=\"grid\" style=\"height: 247px;\" summary=\"This figure shows the steps to factor negative 8 y minus 24. The first step ignores the negative sign and finds the G C F of the two terms 8 y and 24. These factors are written in two rows. The first row is 8 y = 2 times 2 times 2 times y. The second row is 24 = 2 times 2 times 2 times 3. The common factors in these two rows are circled 2, 2, 2. Below these rows is the statement G C F = 2 times 2 times 2 and the statement G C F = 8. Below this is the expression negative 8 y \u2013 24. Then each term is factored negative 8 times y plus negative 8 times 3. The factored expression is written negative 8 times (y plus 3). Under this the expression negative 8 times (y plus 3) is multiplied to check. The product is negative 8 y minus 24.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 128px;\">\n<td style=\"height: 128px; width: 965.483px;\">Ignoring the signs of the terms, we first find the GCF of 8<em data-effect=\"italics\">y<\/em> and 24 is 8. Since the expression \u22128<em data-effect=\"italics\">y<\/em> \u2212 24 has a negative leading coefficient, we use \u22128 as the GCF.<\/td>\n<td style=\"height: 128px; width: 159.119px;\"><span id=\"eip-id1172187954772\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 40px;\">\n<td style=\"height: 40px; width: 965.483px;\" data-valign=\"top\">Rewrite each term using the GCF.<\/td>\n<td style=\"height: 40px; width: 159.119px;\"><span id=\"eip-id1172187954788\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\n<span id=\"eip-id1172183298209\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 965.483px;\">Factor the GCF.<\/td>\n<td style=\"height: 19px; width: 159.119px;\"><span id=\"eip-id1172183298226\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\">Check.<\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ffba55c0b090228658ae4c2d34e81b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dbe3dc8cbfdc88527e2c624720284ad4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 159.119px;\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 965.483px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-056ba6ff3086aaf9d671f5ab22d7724e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#121;&#45;&#50;&#52;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1168345676373\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345676376\" data-type=\"exercise\">\n<div id=\"fs-id1168345695257\" data-type=\"problem\">\n<p id=\"fs-id1168345695259\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1c728fc18d93ee165d06ad7394093f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#122;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"79\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345486693\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345486695\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90036ef6e621caa9647467df9a308158_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#122;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" 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 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345406591\" data-type=\"problem\">\n<p id=\"fs-id1168345406593\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e114eca88082be70c3262b23841d8e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#121;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"71\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341857624\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345530237\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-050630913790584c1d7447fbfc0ad10a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345517560\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345406589\" data-type=\"exercise\">\n<div id=\"fs-id1168341857624\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345517773\" data-type=\"problem\">\n<p id=\"fs-id1168345525318\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eaa5213c7df2df4a09fe2dc76c73facf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#54;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345453838\" 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-id1168342171012\">The leading coefficient is negative, so the GCF will be negative.?<\/p>\n<table id=\"eip-id1172183451275\" class=\"grid\" summary=\"This figure shows the steps to factor negative 6 a 2 plus 36 a. The first step ignores the negative sign and finds the G C F of the two terms 6 a 2 and 36 a. These factors are written in two rows. The first row is 6 a 2 = 2 times 3 times a times a. The second row is 36 a = 2 times 2 times 3 times 3 times a. The common factors in these two rows are circled 2, 3, a. Below these rows is the statement G C F = 2 times 3 times a and the statement G C F = 6 a. Below this is the expression negative 6 a 2 plus 36 a. Then each term is factored negative 6 a times a minus negative 6 a times 6. The factored expression is written negative 6 a times (a minus 6). Under this the expression negative 6 a(a minus 6) is multiplied to check. The product is negative 6 a 2 plus 36 a.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\">Since the leading coefficient is negative, the GCF is negative, \u22126<em data-effect=\"italics\">a<\/em>.<\/td>\n<td><span id=\"eip-id1172183451295\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\n<span id=\"fs-id1167267738277\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite each term using the GCF.<\/td>\n<td><span id=\"eip-id1172183411347\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Factor the GCF.<\/td>\n<td><span id=\"eip-id1172183411364\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aac857ed411c34e94bc9728c26402c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a4b938fd1be68fe6aeb5ab24fb7130ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"160\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d590948107658406fc7636015bda9952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#54;&#97;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345451505\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345451508\" data-type=\"exercise\">\n<div id=\"fs-id1168342104232\" data-type=\"problem\">\n<p id=\"fs-id1168342104234\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30bdbce3999cad38d680826ab6282872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#54;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345530191\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345530193\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ac043128409aac188f65e005bcef5ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" 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 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345578926\" data-type=\"problem\">\n<p id=\"fs-id1168345578928\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cb476e3611bd844b6e3041be596ea06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341861254\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168341861256\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b35f005945d55f8ac91f9b597d15bd5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342180636\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345578924\" data-type=\"exercise\">\n<div id=\"fs-id1168341861254\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345414772\" data-type=\"problem\">\n<p id=\"fs-id1168345414774\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c773c7a71e4b309360cd36e539c1945a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#113;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"159\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341906548\" 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-id1168345423614\">The GCF is the binomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b155cced3f88a65d2914e6fe56a8b5f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"fs-id1167271086070\" class=\"grid\" summary=\"This figure has the steps to factor 5 q times (q plus 7) minus 6 times (q plus 7). The first row has the expression 5 q times (q plus 7) minus 6 times (q plus 7) with the (q plus 7) factors labeled as the G C F. Then, the complete factoring, (q + 7) times (5 q minus 6). Check on your own by multiplying.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 330.938px;\"><\/td>\n<td style=\"width: 225.483px;\"><span id=\"fs-id1167270994367\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 330.938px;\">Factor the GCF, (<em data-effect=\"italics\">q<\/em> + 7).<\/td>\n<td style=\"width: 225.483px;\"><span id=\"fs-id1167271010385\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 330.938px;\">Check on your own by multiplying.<\/td>\n<td style=\"width: 225.483px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342180734\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345724061\" data-type=\"exercise\">\n<div id=\"fs-id1168345724063\" data-type=\"problem\">\n<p id=\"fs-id1168345724065\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a92d9ba407c86cbfc54e6f6f4ab733b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"180\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345543440\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345543442\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc03cfbff16f26f03f2dfb8dee041ad2_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;&#52;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" 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 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345521993\" data-type=\"problem\">\n<p id=\"fs-id1168345521995\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c96e9f06de1b34e7a010462307de9b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#110;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"165\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345439500\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345439502\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebb762b5f8b779a4a694259028f5f5b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#110;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Factor by Grouping<\/h1>\n<p id=\"fs-id1168345688046\">When there is no common factor of all the terms of a polynomial, look for a common factor in just some of the terms. When there are four terms, a good way to start is by separating the polynomial into two parts with two terms in each part. Then look for the GCF in each part. If the polynomial can be factored, you will find a common factor emerges from both parts.<\/p>\n<p id=\"fs-id1168345423454\">(Not all polynomials can be factored. Just like some numbers are prime, some polynomials are prime.)<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Factor by Grouping<\/div>\n<div id=\"fs-id1168345423460\" data-type=\"exercise\">\n<div id=\"fs-id1168341915998\" data-type=\"problem\">\n<p id=\"fs-id1168341916003\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f82512021401e9e9d9306cfb2bb63fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;&#43;&#51;&#121;&#43;&#50;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"131\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345386334\" 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-id1168345439520\" data-type=\"media\" data-alt=\"This table gives the steps for factoring x y + 3 y + 2 x + 6. In the first row there is the statement, \u201cgroup terms with common factors\u201d. In the next column, there is the statement of no common factors of all 4 terms. The last column shows the first two terms grouped and the last two terms grouped.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015a_img_new.jpg\" alt=\"This table gives the steps for factoring x y + 3 y + 2 x + 6. In the first row there is the statement, \u201cgroup terms with common factors\u201d. In the next column, there is the statement of no common factors of all 4 terms. The last column shows the first two terms grouped and the last two terms grouped.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345517636\" data-type=\"media\" data-alt=\"The second row has the statement, \u201cfactor out the common factor from each group\u201d. The second column in the second row states to factor out the GCF from the two separate groups. The third column in the second row has the expression y(x + 3) + 2(x + 3).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015b_img_new.jpg\" alt=\"The second row has the statement, \u201cfactor out the common factor from each group\u201d. The second column in the second row states to factor out the GCF from the two separate groups. The third column in the second row has the expression y(x + 3) + 2(x + 3).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168345668202\" data-type=\"media\" data-alt=\"The third row has the statement, \u201cfactor the common factor from the expression\u201d. The second column in this row points out there is a common factor of (x + 3). The third column in the third row shows the factor of (x + 3) factored from the two groups, (x + 3) times (y + 2).\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015c_img_new.jpg\" alt=\"The third row has the statement, \u201cfactor the common factor from the expression\u201d. The second column in this row points out there is a common factor of (x + 3). The third column in the third row shows the factor of (x + 3) factored from the two groups, (x + 3) times (y + 2).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168341917603\" data-type=\"media\" data-alt=\"The last row has the statement, \u201ccheck\u201d. The second column in this row states to multiply (x + 3)(y + 2). The product is shown in the last column of the original polynomial x y + 3 y + 2 x + 6.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_Elem20Alg_Figure_07_01_015d_img_new.jpg\" alt=\"The last row has the statement, \u201ccheck\u201d. The second column in this row states to multiply (x + 3)(y + 2). The product is shown in the last column of the original polynomial x y + 3 y + 2 x + 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345487406\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171632\" data-type=\"exercise\">\n<div id=\"fs-id1168342171634\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345487406\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171632\" data-type=\"exercise\">\n<div id=\"fs-id1168342171634\" data-type=\"problem\">\n<p id=\"fs-id1168342171636\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8504c220cd37116ad3e932e8c3d0071c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;&#43;&#56;&#121;&#43;&#51;&#120;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"140\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168341923798\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168341923800\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-787810279666495a476a694333e97e39_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;&#121;&#43;&#51;&#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<div id=\"fs-id1168345745008\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345745011\" data-type=\"exercise\">\n<div id=\"fs-id1168345486734\" data-type=\"problem\"><\/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 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345486734\" data-type=\"problem\">\n<p id=\"fs-id1168345486736\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92cc44e6766dc695b836b585e38bd915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;&#43;&#55;&#98;&#43;&#56;&#97;&#43;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"135\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345466322\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345708214\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bb6142f3f65f4b6ce80ab546a888b79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#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 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<p>Factor by grouping.<\/p>\n<ol>\n<li>Group terms with common factors.<\/li>\n<li>Factor out the common factor in each group.<\/li>\n<li>Factor the common factor from the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168341852746\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341962937\" data-type=\"problem\">\n<p id=\"fs-id1168341962939\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dd71a81fca0b0f73f0a45c736d4428e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345424536\" data-type=\"solution\">\n<div data-type=\"title\">\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">There is no GCF in all four terms.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dd71a81fca0b0f73f0a45c736d4428e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Separate into two parts.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a954a6701f24efd87241755033531bc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#125;&#92;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#123;&#45;&#50;&#120;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"127\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-875eb8643d1a58f62d2b4a188e0b72fc_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;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"155\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Check on your own by multiplying.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345466016\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341906472\" data-type=\"exercise\">\n<div id=\"fs-id1168341906474\" data-type=\"problem\">\n<p id=\"fs-id1168341906476\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a36387e88bca237ae2078846ca3849a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#53;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345661386\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345661388\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-34a31a4033d905a5781ed903f19b5b54_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;&#43;&#50;&#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>\n<div id=\"fs-id1168345630365\" class=\"media-2\" data-type=\"note\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342171747\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342171751\" data-type=\"exercise\">\n<div id=\"fs-id1168345385682\" data-type=\"problem\">\n<p id=\"fs-id1168345385684\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a6b6bec08aa5bcea0aa800a250fe648_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#121;&#45;&#55;&#121;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345558127\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1168345558129\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c6135dc1bcd04883aac4fe206b5ddb4_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;&#55;&#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>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345630368\">Access these online resources for additional instruction and practice with greatest common factors (GFCs) and factoring by grouping.<\/p>\n<ul id=\"fs-id1168345386819\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25GCF1\">Greatest Common Factor (GCF)<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25GCF2\">Factoring Out the GCF of a Binomial<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25GCF3\">Greatest Common Factor (GCF) of Polynomials<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1168345558554\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Finding the Greatest Common Factor (GCF):<\/strong> To find the GCF of two expressions:\n<ol id=\"fs-id1168745400837\" class=\"stepwise\" type=\"1\">\n<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n<li>Bring down the common factors that all expressions share.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Factor the Greatest Common Factor from a Polynomial:<\/strong> To factor a greatest common factor from a polynomial:\n<ol id=\"fs-id1168741805522\" class=\"stepwise\" type=\"1\">\n<li>Find the GCF of all the terms of the polynomial.<\/li>\n<li>Rewrite each term as a product using the GCF.<\/li>\n<li>Use the \u2018reverse\u2019 Distributive Property to factor the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Factor by Grouping:<\/strong> To factor a polynomial with 4 four or more terms\n<ol id=\"fs-id1168745075740\" class=\"stepwise\" type=\"1\">\n<li>Group terms with common factors.<\/li>\n<li>Factor out the common factor in each group.<\/li>\n<li>Factor the common factor from the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1168345539526\">\n<dt>factoring<\/dt>\n<dd id=\"fs-id1168345539531\">Factoring is splitting a product into factors; in other words, it is the reverse process of multiplying.<\/dd>\n<\/dl>\n<dl id=\"fs-id1168345448206\">\n<dt>greatest common factor<\/dt>\n<dd id=\"fs-id1168345448211\">The greatest common factor is the largest expression that is a factor of two or more expressions is the greatest common factor (GCF).<\/dd>\n<\/dl>\n<p>Type your textbox content here.<\/p>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Find the Greatest Common Factor of Two or More Expressions<\/h2>\n<p id=\"fs-id1168741931620\">In the following exercises, find the greatest common factor.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 126px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">1. 8, 18<\/td>\n<td style=\"width: 50%; height: 14px;\">2. 24, 40<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">3. 72, 162<\/td>\n<td style=\"width: 50%; height: 14px;\">4. 150, 275<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">5. 10<em data-effect=\"italics\">a<\/em>, 50<\/td>\n<td style=\"width: 50%; height: 14px;\">6. 5<em data-effect=\"italics\">b<\/em>, 30<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c651aa64bc9353b7c563c7ceeb1cdf48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#44;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-502587740b882a87cfc39c80151cf7f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#52;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12dd42fdb990feb5838d106ec07de9f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#44;&#50;&#52;&#123;&#119;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d14e7e3c9224a4f349138ea82a7cc933_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2224b35f321d743c142c9e08fd66a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#113;&#44;&#49;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8abb0a2670da3e0019cba6a1d0b697a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#48;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-499a2e83cae0d27186b4fdf269cc4fbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#44;&#51;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d99519b10440c37d8b2d47aa4d560bb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#44;&#52;&#50;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4c1ecf041279c2ab3ea5c40816c372e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#52;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf20ba1476230af9371f18125364c567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#50;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1eaeb6f94e37aa18f1bc8ffdbefd9b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19b538cbe191e01c43e9a3ffb4a73054_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#53;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Factor the Greatest Common Factor from a Polynomial<\/h2>\n<p id=\"fs-id1168745121996\">In the following exercises, factor the greatest common factor from each polynomial.<\/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;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a974c99b6e476658bde7b78ed63a575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e88a9acb694ed734d8b5b7724a388165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebfe857d6de33f9e98b471b0176838ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#109;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"55\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d7c26f6ceb770a456b95a0a1aedbc80a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#112;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49d7e7874e0a23b6a3107040e57a89ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#113;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72498aed2a5a43227ec2c82da306c8d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#114;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e58ccaafeb8351e6eeb645a4aa01c0cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#109;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fa3700d696b14f882a66f8056a5b7fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#110;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-754b39a85b11f41442c53267d6511936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#110;&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd64d1ac24d4d85e33e2d92d2189ad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#98;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d37daec7b49c49d44e3ccbf85670901a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-664a2a337a922fc07d53def43034f474_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fb8ab118fa6c57bb8651b54ccc4a5b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#112;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-682d7dee7eef2acb05dc225900b7d61e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#113;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2fc87bb5a60031b988b2e31f1fd60de7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72e96a2d5a9f782b0e9bb64c649df850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"84\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38489720e01153e829082926006d7ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-efa01d1e1d08c12e89758796547e35cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#48;&#109;&#43;&#49;&#54;\" 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;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2372f97c3c20427befc26c33c33fdc24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ddafecf3466c9e382ed31d987687746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#53;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#56;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -4px;\" \/><\/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-18d5a3608b5d8e24bad24023e3d124d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">40 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b90c960e0ada8a6825284fdacdfdde19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#98;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: -2px;\" \/><\/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-912ad698e4a6f749ed76db5820d979c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"164\" 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-0ef969c3be0317da851686894ce1fe9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"164\" 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-e943f389eb4d1ec83b695c1aa673ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"165\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8690439c21e9459d0cd0370bafd3df8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"180\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Factor by Grouping<\/h2>\n<p id=\"fs-id1168745400658\">In the following exercises, factor by grouping.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe20a7f7e67629a977b4129c17ca0911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;&#43;&#50;&#121;&#43;&#51;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"131\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8cfbb7ed4bee4a100d4ea60eeff601ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#110;&#43;&#52;&#110;&#43;&#54;&#109;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"153\" 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-f68f08093e98f9086280ff4a0d94ffb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#118;&#45;&#57;&#117;&#43;&#50;&#118;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff0cd233d3353d014245e9844c5c8d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#113;&#45;&#49;&#48;&#112;&#43;&#56;&#113;&#45;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/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-1cf5e138aeb37f9181cd7abff9368482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#98;&#45;&#52;&#98;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" 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-745c5ef6a220cba706687a22be8a401a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#109;&#45;&#49;&#50;&#109;&#45;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"163\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91ef56942ba52ce2b83da2868a7d3a90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#112;&#45;&#57;&#112;&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2696999c22e77980c87e86925c57b716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#51;&#120;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"138\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Mixed Practice<\/h2>\n<p id=\"fs-id1168741893632\">In the following exercises, factor.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4afacae05befc91a1823a9bd9d0f6891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"80\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1e07a5d3a71955d5a0d882fee34fa6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35bb8f42ba167dfcb8f85e920d3411f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-10b2afa2e15afa7ce8bf446e0883f1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/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-7b3e85e578b5c0d68a557b3f0b7577b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#121;&#43;&#53;&#120;&#43;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20aa56aa0d0574d3c1c4e1c8b0615ed5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"146\" style=\"vertical-align: 0px;\" \/><\/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%;\">59.<strong data-effect=\"bold\"> Area of a rectangle<\/strong> The area of a rectangle with length 6 less than the width is given by the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bea491c7df552a76e56be315c554e96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba9af47bcc105aa4e2879c231fa76d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"31\" style=\"vertical-align: 0px;\" \/> width. Factor the greatest common factor from the polynomial.<\/td>\n<td style=\"width: 50%;\">60. <strong data-effect=\"bold\">Height of a baseball<\/strong> The height of a baseball <em data-effect=\"italics\">t<\/em> seconds after it is hit is given by the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7361f6adc5fb931833dd4707602de3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#48;&#116;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"121\" style=\"vertical-align: -2px;\" \/>. Factor the greatest common factor from the polynomial.<\/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%;\">61. The greatest common factor of 36 and 60 is 12. Explain what this means.<\/td>\n<td style=\"width: 50%;\">62. What is the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-626101b8179886545cbbb76a3d417034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#44;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18f0c771be0f5f7f94a86466c8873ac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -4px;\" \/>? Write a general rule that tells you how to find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a7829847dcae716e584dfe82697fc2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#97;&#125;&#44;&#123;&#121;&#125;&#94;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5fbc2e8afd714f4a7e4ba156b46965e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"15\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 192px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">1. 2<\/td>\n<td style=\"width: 50%; height: 16px;\">3. 18<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">5. 10<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/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-b5e78bed819747599f8b91ef2609f971_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#119;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/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-d8d1e8e2f094da0cc218fc1de808d7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#112;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" 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-e474101f81c4119eea53625fd801e3ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/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-02baaffe4ddb6a44400eb7ba175e566c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/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-0ad8655a65bb986a62c563c119edd22c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/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-ab86532cd874a9dc41de09db45872374_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" 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-25dc6a998bfa12795f326b9b7e77e356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" 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-a514d308a678cd90cab1b339537bcc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" 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-4b58ad360c7cd525d242278b6d4c653c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"71\" 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-e478a99f4856e944f6d9b432f1d9ccf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-10eac7b8a8b138c0e7d072602c133cf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -7px;\" \/><\/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-4f8ccb29118d92ac678ae351e9d2ff09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#112;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"122\" style=\"vertical-align: -7px;\" \/><\/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-c26c3e186a9b8a7920dfcae93bc32aed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-f3c485d163455c737d76c631684bd78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -7px;\" \/><\/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-5aaeebf77da166451d623c11c5e3fa9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -7px;\" \/><\/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-8891c01a67d1fc2d613481a3843b9c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4d80d20184793c185b79356551ccc0c_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;&#53;&#120;&#43;&#51;&#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;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8317f1be24973878632079adac21daa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#98;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"123\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cfa55370abe441dc386d418fe405a728_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;&#120;&#43;&#50;&#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;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f934eecebf8aae99d1fa0d7a022814c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/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-d4982a022c3a967fdd19a192f84e7c0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-345d2ef4a891d639106a94c4ebc18d51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#52;&#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>\n<td style=\"width: 50%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38a805bd7c1719aef4a27872eef0eab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" 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-f7a0520e3748fd3ccf7900c553224f56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/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-b20510bf55410adad55d86d2e634bcaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-961263bd200559a5e00c571f22ec98b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61.\u00a0Answers will vary.<\/td>\n<td style=\"width: 50%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cGreatest Common Factor and Factor by Grouping\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.<!-- pb_fixme --><\/p>\n","protected":false},"author":90,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2258","chapter","type-chapter","status-publish","hentry"],"part":2016,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2258","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\/2258\/revisions"}],"predecessor-version":[{"id":2522,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2258\/revisions\/2522"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/2016"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2258\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=2258"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=2258"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=2258"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=2258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}