{"id":315,"date":"2015-09-18T21:15:10","date_gmt":"2015-09-18T21:15:10","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=315"},"modified":"2015-11-03T23:39:23","modified_gmt":"2015-11-03T23:39:23","slug":"key-concepts-glossary-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/key-concepts-glossary-5\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Equations<\/h2>\r\n<table><caption>\u00a0<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong>difference of squares<\/strong><\/td>\r\n<td>[latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>perfect square trinomial<\/strong><\/td>\r\n<td>[latex]{a}^{2}+2ab+{b}^{2}={\\left(a+b\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>sum of cubes<\/strong><\/td>\r\n<td>[latex]{a}^{3}+{b}^{3}=\\left(a+b\\right)\\left({a}^{2}-ab+{b}^{2}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>difference of cubes<\/strong><\/td>\r\n<td>[latex]{a}^{3}-{b}^{3}=\\left(a-b\\right)\\left({a}^{2}+ab+{b}^{2}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul>\r\n\t<li>The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem.<\/li>\r\n\t<li>Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term.<\/li>\r\n\t<li>Trinomials can be factored using a process called factoring by grouping.<\/li>\r\n\t<li>Perfect square trinomials and the difference of squares are special products and can be factored using equations.<\/li>\r\n\t<li>The sum of cubes and the difference of cubes can be factored using equations.<\/li>\r\n\t<li>Polynomials containing fractional and negative exponents can be factored by pulling out a GCF.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>factor by grouping\u00a0<\/strong>a method for factoring a trinomial in the form [latex]a{x}^{2}+bx+c[\/latex] by dividing the <em data-effect=\"italics\">x<\/em> term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression\r\n\r\n<strong>greatest common factor\u00a0<\/strong>the largest polynomial that divides evenly into each polynomial\r\n\r\n&nbsp;","rendered":"<h2>Key Equations<\/h2>\n<table>\n<caption>\u00a0<\/caption>\n<tbody>\n<tr>\n<td><strong>difference of squares<\/strong><\/td>\n<td>[latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>perfect square trinomial<\/strong><\/td>\n<td>[latex]{a}^{2}+2ab+{b}^{2}={\\left(a+b\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>sum of cubes<\/strong><\/td>\n<td>[latex]{a}^{3}+{b}^{3}=\\left(a+b\\right)\\left({a}^{2}-ab+{b}^{2}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>difference of cubes<\/strong><\/td>\n<td>[latex]{a}^{3}-{b}^{3}=\\left(a-b\\right)\\left({a}^{2}+ab+{b}^{2}\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem.<\/li>\n<li>Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term.<\/li>\n<li>Trinomials can be factored using a process called factoring by grouping.<\/li>\n<li>Perfect square trinomials and the difference of squares are special products and can be factored using equations.<\/li>\n<li>The sum of cubes and the difference of cubes can be factored using equations.<\/li>\n<li>Polynomials containing fractional and negative exponents can be factored by pulling out a GCF.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>factor by grouping\u00a0<\/strong>a method for factoring a trinomial in the form [latex]a{x}^{2}+bx+c[\/latex] by dividing the <em data-effect=\"italics\">x<\/em> term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression<\/p>\n<p><strong>greatest common factor\u00a0<\/strong>the largest polynomial that divides evenly into each polynomial<\/p>\n<p>&nbsp;<\/p>\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-315\">\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>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":276,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-315","chapter","type-chapter","status-publish","hentry"],"part":205,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/315\/revisions"}],"predecessor-version":[{"id":582,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/315\/revisions\/582"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/205"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/315\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=315"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=315"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=315"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}