{"id":16303,"date":"2019-10-03T03:06:08","date_gmt":"2019-10-03T03:06:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/lesson-2-factoring-polynomials\/"},"modified":"2020-10-22T09:32:00","modified_gmt":"2020-10-22T09:32:00","slug":"lesson-2-factoring-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/lesson-2-factoring-polynomials\/","title":{"raw":"13.2 - Introduction to Factoring Methods","rendered":"13.2 &#8211; Introduction to Factoring Methods"},"content":{"raw":"<h2>What you'll learn to do: Use factoring methods to find the binomial factors of a polynomial.<\/h2>\r\nOne of the most important and powerful concepts that we use in mathematics is that of complementary operations. \u00a0We already learned that subtraction can \"undo\" addition, and multiplication can \"undo\" division. \u00a0These ideas helped us solve equations, find the slope of a line, and write a two variable linear equation iso that we could\u00a0graph it easily. In the last unit, we learned that the techniques we learned for solving linear equations didn't apply to solving polynomial equations, so we factored\u00a0the polynomials and used the zero products principle. So far, we've worked with polynomials that factored into the product of a monomial and a binomial. \u00a0In this section we will focus on learning how to factor a polynomial that results in the product of two binomials. Factoring \"undoes\" multiplication of polynomials.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_4816\" align=\"alignnone\" width=\"417\"]<img class=\"wp-image-4816\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/11211929\/Screen-Shot-2016-06-11-at-2.18.48-PM-300x224.png\" alt=\"Keyboard button with the word &quot;undo&quot; on it\" width=\"417\" height=\"311\" \/> Undo[\/caption]\r\n\r\n&nbsp;\r\n\r\nSpecifically, in this section you\u2019ll learn how to:\r\n<ul>\r\n \t<li>Factor a four term polynomial by grouping terms<\/li>\r\n \t<li>Apply an algorithm to rewrite a trinomial as a four term polynomial<\/li>\r\n \t<li>Using factoring by grouping to factor a trinomial<\/li>\r\n \t<li>Factor trinomials of the form\u00a0[latex]ax^2+bx+c[\/latex]<\/li>\r\n \t<li>Factor a trinomial with a leading coefficient of 1<\/li>\r\n \t<li>Use a shortcut to factor trinomials of the form [latex]x^2+bx+c[\/latex]<\/li>\r\n<\/ul>","rendered":"<h2>What you&#8217;ll learn to do: Use factoring methods to find the binomial factors of a polynomial.<\/h2>\n<p>One of the most important and powerful concepts that we use in mathematics is that of complementary operations. \u00a0We already learned that subtraction can &#8220;undo&#8221; addition, and multiplication can &#8220;undo&#8221; division. \u00a0These ideas helped us solve equations, find the slope of a line, and write a two variable linear equation iso that we could\u00a0graph it easily. In the last unit, we learned that the techniques we learned for solving linear equations didn&#8217;t apply to solving polynomial equations, so we factored\u00a0the polynomials and used the zero products principle. So far, we&#8217;ve worked with polynomials that factored into the product of a monomial and a binomial. \u00a0In this section we will focus on learning how to factor a polynomial that results in the product of two binomials. Factoring &#8220;undoes&#8221; multiplication of polynomials.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"attachment_4816\" style=\"width: 427px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4816\" class=\"wp-image-4816\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/11211929\/Screen-Shot-2016-06-11-at-2.18.48-PM-300x224.png\" alt=\"Keyboard button with the word &quot;undo&quot; on it\" width=\"417\" height=\"311\" \/><\/p>\n<p id=\"caption-attachment-4816\" class=\"wp-caption-text\">Undo<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Specifically, in this section you\u2019ll learn how to:<\/p>\n<ul>\n<li>Factor a four term polynomial by grouping terms<\/li>\n<li>Apply an algorithm to rewrite a trinomial as a four term polynomial<\/li>\n<li>Using factoring by grouping to factor a trinomial<\/li>\n<li>Factor trinomials of the form\u00a0[latex]ax^2+bx+c[\/latex]<\/li>\n<li>Factor a trinomial with a leading coefficient of 1<\/li>\n<li>Use a shortcut to factor trinomials of the form [latex]x^2+bx+c[\/latex]<\/li>\n<\/ul>\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-16303\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Screenshot: Undo. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Outcomes and Description. <strong>Provided by<\/strong>: Lumen Learning. <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":169554,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Screenshot: Undo\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Outcomes and Description\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"8076008d880d480494979e137e1b2ada","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-16303","chapter","type-chapter","status-publish","hentry"],"part":16188,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16303","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/169554"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16303\/revisions"}],"predecessor-version":[{"id":20414,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16303\/revisions\/20414"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/16188"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16303\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=16303"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=16303"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=16303"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=16303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}