{"id":10893,"date":"2017-06-05T21:41:01","date_gmt":"2017-06-05T21:41:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10893"},"modified":"2017-09-24T05:40:13","modified_gmt":"2017-09-24T05:40:13","slug":"summary-factoring-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/summary-factoring-polynomials\/","title":{"raw":"Summary: Factoring Polynomials","rendered":"Summary: Factoring Polynomials"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-186\">\r\n \t<li><strong>Find the greatest common factor.<\/strong>\r\n<ol id=\"eip-id1170326457882\" class=\"stepwise\">\r\n \t<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\r\n \t<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\r\n \t<li>Bring down the common factors that all expressions share.<\/li>\r\n \t<li>Multiply the factors.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Distributive Property<\/strong>\r\n<ul id=\"eip-id1170326285964\">\r\n \t<li>If [latex]a[\/latex] , [latex]b[\/latex] , [latex]c[\/latex] are real numbers, then[latex]a\\left(b+c\\right)=ab+ac[\/latex] and [latex]ab+ac=a\\left(b+c\\right)[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Factor the greatest common factor from a polynomial.<\/strong>\r\n<ol id=\"eip-id1170326292744\" class=\"stepwise\">\r\n \t<li>Find the GCF of all the terms of the polynomial.<\/li>\r\n \t<li>Rewrite each term as a product using the GCF.<\/li>\r\n \t<li>Use the Distributive Property \u2018in reverse\u2019 to factor the expression.<\/li>\r\n \t<li>Check by multiplying the factors.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1164354639880\" class=\"definition\">\r\n \t<dt>greatest common factor<\/dt>\r\n \t<dd id=\"fs-id1164354639885\">The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/dd>\r\n<\/dl>\r\n<h2><\/h2>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-186\">\n<li><strong>Find the greatest common factor.<\/strong>\n<ol id=\"eip-id1170326457882\" class=\"stepwise\">\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>Distributive Property<\/strong>\n<ul id=\"eip-id1170326285964\">\n<li>If [latex]a[\/latex] , [latex]b[\/latex] , [latex]c[\/latex] are real numbers, then[latex]a\\left(b+c\\right)=ab+ac[\/latex] and [latex]ab+ac=a\\left(b+c\\right)[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Factor the greatest common factor from a polynomial.<\/strong>\n<ol id=\"eip-id1170326292744\" class=\"stepwise\">\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 Distributive Property \u2018in reverse\u2019 to factor the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1164354639880\" class=\"definition\">\n<dt>greatest common factor<\/dt>\n<dd id=\"fs-id1164354639885\">The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/dd>\n<\/dl>\n<h2><\/h2>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10893\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21046,"menu_order":30,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"c24142af-9c95-4212-9f7c-c4d93b464d75","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10893","chapter","type-chapter","status-publish","hentry"],"part":8336,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10893","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/21046"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10893\/revisions"}],"predecessor-version":[{"id":15185,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10893\/revisions\/15185"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/8336"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10893\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=10893"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10893"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=10893"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=10893"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}