{"id":1383,"date":"2021-12-02T19:37:45","date_gmt":"2021-12-03T00:37:45","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/7-7-choosing-the-correct-factoring-strategy\/"},"modified":"2023-08-30T18:36:36","modified_gmt":"2023-08-30T22:36:36","slug":"choosing-the-correct-factoring-strategy","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/choosing-the-correct-factoring-strategy\/","title":{"raw":"7.7 Choosing the Correct Factoring Strategy","rendered":"7.7 Choosing the Correct Factoring Strategy"},"content":{"raw":"With so many different tools used to factor, it is prudent to have a section to determine the best strategy to factor.\r\n<h2>Factoring Hints<\/h2>\r\n<ol>\r\n \t<li>Look for any factor to simplify the polynomial before you start!<\/li>\r\n \t<li>If you have two terms, look for a sum or difference of squares or cubes.\r\n<ul>\r\n \t<li>[latex]a^2 - b^2 = (a + b)(a - b)[\/latex][latex]a^3 - b^3 = (a - b)(a^2 + ab + b^2)[\/latex][latex]a^3 + b^3 = (a + b)(a^2 - ab + b2)[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>If you have three terms, see if the master product method works.<\/li>\r\n \t<li>If you have four terms, see if factoring by grouping works.<\/li>\r\n<\/ol>\r\nIf you find that you have trouble factoring the questions in this section, then you might need to redo from the start of Chapter 7. This is not uncommon.\r\n<h1>Questions<\/h1>\r\nFactor each completely.\r\n<ol class=\"twocolumn\">\r\n \t<li>[latex]24ac-18ab+60dc-45db[\/latex]<\/li>\r\n \t<li>[latex]2x^2-11x+15[\/latex]<\/li>\r\n \t<li>[latex]5u^2-9uv+4v^2[\/latex]<\/li>\r\n \t<li>[latex]16x^2+48xy+36y^2[\/latex]<\/li>\r\n \t<li>[latex]-2x^3+128y^3[\/latex]<\/li>\r\n \t<li>[latex]20uv-60u^3-5xv+15xu^2[\/latex]<\/li>\r\n \t<li>[latex]54u^3-16[\/latex]<\/li>\r\n \t<li>[latex]54-128x^3[\/latex]<\/li>\r\n \t<li>[latex]n^2-n[\/latex]<\/li>\r\n \t<li>[latex]5x^2-22x-15[\/latex]<\/li>\r\n \t<li>[latex]x^2-4xy+3y^2[\/latex]<\/li>\r\n \t<li>[latex]45u^2-150uv+125v^2[\/latex]<\/li>\r\n \t<li>[latex]m^2-4n^2[\/latex]<\/li>\r\n \t<li>[latex]12ab-18a+6nb-9n[\/latex]<\/li>\r\n \t<li>[latex]36b^2c-16ad-24b^2d+24ac[\/latex]<\/li>\r\n \t<li>[latex]3m^3-6m^2n-24n^2m[\/latex]<\/li>\r\n \t<li>[latex]128+54x^3[\/latex]<\/li>\r\n \t<li>[latex]64m^3+27n^3[\/latex]<\/li>\r\n \t<li>[latex]n^3+7n^2+10n[\/latex]<\/li>\r\n \t<li>[latex]64m^3-n^3[\/latex]<\/li>\r\n \t<li>[latex]27x^3-64[\/latex]<\/li>\r\n \t<li>[latex]16a^2-9b^2[\/latex]<\/li>\r\n \t<li>[latex]5x^2+2x[\/latex]<\/li>\r\n \t<li>[latex]2x^2-10x+12[\/latex]<\/li>\r\n<\/ol>\r\n<a class=\"internal\" href=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-7\/\">Answer Key 7.7<\/a>","rendered":"<p>With so many different tools used to factor, it is prudent to have a section to determine the best strategy to factor.<\/p>\n<h2>Factoring Hints<\/h2>\n<ol>\n<li>Look for any factor to simplify the polynomial before you start!<\/li>\n<li>If you have two terms, look for a sum or difference of squares or cubes.\n<ul>\n<li>[latex]a^2 - b^2 = (a + b)(a - b)[\/latex][latex]a^3 - b^3 = (a - b)(a^2 + ab + b^2)[\/latex][latex]a^3 + b^3 = (a + b)(a^2 - ab + b2)[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>If you have three terms, see if the master product method works.<\/li>\n<li>If you have four terms, see if factoring by grouping works.<\/li>\n<\/ol>\n<p>If you find that you have trouble factoring the questions in this section, then you might need to redo from the start of Chapter 7. This is not uncommon.<\/p>\n<h1>Questions<\/h1>\n<p>Factor each completely.<\/p>\n<ol class=\"twocolumn\">\n<li>[latex]24ac-18ab+60dc-45db[\/latex]<\/li>\n<li>[latex]2x^2-11x+15[\/latex]<\/li>\n<li>[latex]5u^2-9uv+4v^2[\/latex]<\/li>\n<li>[latex]16x^2+48xy+36y^2[\/latex]<\/li>\n<li>[latex]-2x^3+128y^3[\/latex]<\/li>\n<li>[latex]20uv-60u^3-5xv+15xu^2[\/latex]<\/li>\n<li>[latex]54u^3-16[\/latex]<\/li>\n<li>[latex]54-128x^3[\/latex]<\/li>\n<li>[latex]n^2-n[\/latex]<\/li>\n<li>[latex]5x^2-22x-15[\/latex]<\/li>\n<li>[latex]x^2-4xy+3y^2[\/latex]<\/li>\n<li>[latex]45u^2-150uv+125v^2[\/latex]<\/li>\n<li>[latex]m^2-4n^2[\/latex]<\/li>\n<li>[latex]12ab-18a+6nb-9n[\/latex]<\/li>\n<li>[latex]36b^2c-16ad-24b^2d+24ac[\/latex]<\/li>\n<li>[latex]3m^3-6m^2n-24n^2m[\/latex]<\/li>\n<li>[latex]128+54x^3[\/latex]<\/li>\n<li>[latex]64m^3+27n^3[\/latex]<\/li>\n<li>[latex]n^3+7n^2+10n[\/latex]<\/li>\n<li>[latex]64m^3-n^3[\/latex]<\/li>\n<li>[latex]27x^3-64[\/latex]<\/li>\n<li>[latex]16a^2-9b^2[\/latex]<\/li>\n<li>[latex]5x^2+2x[\/latex]<\/li>\n<li>[latex]2x^2-10x+12[\/latex]<\/li>\n<\/ol>\n<p><a class=\"internal\" href=\"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-7\/\">Answer Key 7.7<\/a><\/p>\n","protected":false},"author":90,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1383","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":1369,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1383\/revisions"}],"predecessor-version":[{"id":2128,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1383\/revisions\/2128"}],"part":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1369"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1383\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1383"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapter-type?post=1383"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1383"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}