{"id":607,"date":"2019-04-29T16:00:23","date_gmt":"2019-04-29T20:00:23","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=chapter&#038;p=607"},"modified":"2019-12-03T17:13:02","modified_gmt":"2019-12-03T22:13:02","slug":"7-7-choosing-the-correct-factoring-strategy","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/chapter\/7-7-choosing-the-correct-factoring-strategy\/","title":{"raw":"7.7 Choosing the Correct Factoring Strategy","rendered":"7.7 Choosing the Correct Factoring Strategy"},"content":{"raw":"[latexpage]\r\n\r\nWith 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>\\(a^2 - b^2\u00a0 =\u00a0 (a + b)(a - b)\\)\\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\\)\\(a^3 + b^3 = (a + b)(a^2 - ab + b2)\\)<\/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>\r\n \t<li>\\(24ac-18ab+60dc-45db\\)<\/li>\r\n \t<li>\\(2x^2-11x+15\\)<\/li>\r\n \t<li>\\(5u^2-9uv+4v^2\\)<\/li>\r\n \t<li>\\(16x^2+48xy+36y^2\\)<\/li>\r\n \t<li>\\(-2x^3+128y^3\\)<\/li>\r\n \t<li>\\(20uv-60u^3-5xv+15xu^2\\)<\/li>\r\n \t<li>\\(54u^3-16\\)<\/li>\r\n \t<li>\\(54-128x^3\\)<\/li>\r\n \t<li>\\(n^2-n\\)<\/li>\r\n \t<li>\\(5x^2-22x-15\\)<\/li>\r\n \t<li>\\(x^2-4xy+3y^2\\)<\/li>\r\n \t<li>\\(45u^2-150uv+125v^2\\)<\/li>\r\n \t<li>\\(m^2-4n^2\\)<\/li>\r\n \t<li>\\(12ab-18a+6nb-9n\\)<\/li>\r\n \t<li>\\(36b^2c-16ad-24b^2d+24ac\\)<\/li>\r\n \t<li>\\(3m^3-6m^2n-24n^2m\\)<\/li>\r\n \t<li>\\(128+54x^3\\)<\/li>\r\n \t<li>\\(64m^3+27n^3\\)<\/li>\r\n \t<li>\\(n^3+7n^2+10n\\)<\/li>\r\n \t<li>\\(64m^3-n^3\\)<\/li>\r\n \t<li>\\(27x^3-64\\)<\/li>\r\n \t<li>\\(16a^2-9b^2\\)<\/li>\r\n \t<li>\\(5x^2+2x\\)<\/li>\r\n \t<li>\\(2x^2-10x+12\\)<\/li>\r\n<\/ol>\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/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><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-a22a0287f7a12bf6b63afc739904f82e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#45;&#32;&#98;&#94;&#50;&#32;&#32;&#61;&#32;&#32;&#40;&#97;&#32;&#43;&#32;&#98;&#41;&#40;&#97;&#32;&#45;&#32;&#98;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-cc3a2aee650a1c966349259b05845daa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#51;&#32;&#45;&#32;&#98;&#94;&#51;&#32;&#61;&#32;&#40;&#97;&#32;&#45;&#32;&#98;&#41;&#40;&#97;&#94;&#50;&#32;&#43;&#32;&#97;&#98;&#32;&#43;&#32;&#98;&#94;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"236\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-3dfd226de6af61b9ddc528fd6eb4522e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#51;&#32;&#43;&#32;&#98;&#94;&#51;&#32;&#61;&#32;&#40;&#97;&#32;&#43;&#32;&#98;&#41;&#40;&#97;&#94;&#50;&#32;&#45;&#32;&#97;&#98;&#32;&#43;&#32;&#98;&#50;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"237\" style=\"vertical-align: -4px;\" \/><\/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>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-71a602c26a45be0260c4e0204e5ee5c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#97;&#99;&#45;&#49;&#56;&#97;&#98;&#43;&#54;&#48;&#100;&#99;&#45;&#52;&#53;&#100;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"204\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-0300b9bac95d3829065103907deff242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#94;&#50;&#45;&#49;&#49;&#120;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"115\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-0f542a516dcef1eb844459c4867ed1c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#117;&#94;&#50;&#45;&#57;&#117;&#118;&#43;&#52;&#118;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-6c573509d15a3d4047223feecf5322c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#120;&#94;&#50;&#43;&#52;&#56;&#120;&#121;&#43;&#51;&#54;&#121;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-f02bbafb5d0155670a3ddedfa50e4051_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#94;&#51;&#43;&#49;&#50;&#56;&#121;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-8cf0f8b08ca127802efb2bfbff93cfa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#117;&#118;&#45;&#54;&#48;&#117;&#94;&#51;&#45;&#53;&#120;&#118;&#43;&#49;&#53;&#120;&#117;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"211\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-9a1cf7342e311dc5b57ea08f72b57180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;&#117;&#94;&#51;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"75\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-2b85f8091e62b252c1ae3ff942a32337_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;&#45;&#49;&#50;&#56;&#120;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-0f81e8980ec7282947cbf1e474acd04f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#94;&#50;&#45;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-48e41a6b49e5700925e191206bd90180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#94;&#50;&#45;&#50;&#50;&#120;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"115\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-8204e453b7e27c97a8e6ba898ef91e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;&#50;&#45;&#52;&#120;&#121;&#43;&#51;&#121;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-3ac2f383c2923fd7acdb12c54b7bc47e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#117;&#94;&#50;&#45;&#49;&#53;&#48;&#117;&#118;&#43;&#49;&#50;&#53;&#118;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"168\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-ff56cc3c0ce8421b0a71267f7585a312_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#94;&#50;&#45;&#52;&#110;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-dad50b0916640d32a1ecfe4be9db2d97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#97;&#98;&#45;&#49;&#56;&#97;&#43;&#54;&#110;&#98;&#45;&#57;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"173\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-c380e5b1bf673ad590396baf7cce1a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#98;&#94;&#50;&#99;&#45;&#49;&#54;&#97;&#100;&#45;&#50;&#52;&#98;&#94;&#50;&#100;&#43;&#50;&#52;&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"219\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-8de274aa90990bc386f3ce1b97692f85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#109;&#94;&#51;&#45;&#54;&#109;&#94;&#50;&#110;&#45;&#50;&#52;&#110;&#94;&#50;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"169\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-8dc703b774d0dee7455a160edf3580c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#56;&#43;&#53;&#52;&#120;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-dc45e1d0a84a879edb1776c3949b3c6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#109;&#94;&#51;&#43;&#50;&#55;&#110;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-395f49509425b69699a2df73a5273c4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#94;&#51;&#43;&#55;&#110;&#94;&#50;&#43;&#49;&#48;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-050fb578d74cb45deba8ebdadf1b3517_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#109;&#94;&#51;&#45;&#110;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-9936c1d53cfe46811c7a908da136ba75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#120;&#94;&#51;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"75\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-3d38dd0a0bfbba16e10feae99f6219d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#97;&#94;&#50;&#45;&#57;&#98;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-10bc773339a3891610a07ea014d6f5cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#94;&#50;&#43;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-content\/ql-cache\/quicklatex.com-ef4d2cfe7d72e2c287f7e883e6d28750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#94;&#50;&#45;&#49;&#48;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"115\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ol>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-7-7\/\">Answer Key 7.7<\/a><\/p>\n","protected":false},"author":540,"menu_order":21,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-607","chapter","type-chapter","status-publish","hentry"],"part":379,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/607","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/540"}],"version-history":[{"count":8,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/607\/revisions"}],"predecessor-version":[{"id":3622,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/607\/revisions\/3622"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/parts\/379"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapters\/607\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=607"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/chapter-type?post=607"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=607"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}