{"id":16324,"date":"2019-10-03T03:21:55","date_gmt":"2019-10-03T03:21:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-special-cases\/"},"modified":"2024-04-30T23:20:37","modified_gmt":"2024-04-30T23:20:37","slug":"outcome-special-cases","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/outcome-special-cases\/","title":{"raw":"Introduction to Factoring Special Cases","rendered":"Introduction to Factoring Special Cases"},"content":{"raw":"<h3>Why Learn How to Factor Special Cases?<\/h3>\r\n<img class=\"size-medium wp-image-2786 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/19191115\/Screen-Shot-2016-07-19-at-12.10.30-PM-300x153.png\" alt=\"Repeated pattern of interlocking plus signs, each row a different color following the rainbow spectrum.\" width=\"300\" height=\"153\" \/>\r\n\r\nSome people like to find patterns in the world around them, like a game. There are some polynomials that, when factored, follow a specific pattern.\r\n\r\nThese include:\r\n\r\nPerfect square trinomials of the form:\u00a0[latex]{a}^{2}+2ab+{b}^{2}[\/latex]\r\n\r\nA difference of squares:\u00a0[latex]{a}^{2}-{b}^{2}[\/latex]\r\n\r\nA sum of cubes:\u00a0[latex]{a}^{3}+{b}^{3}[\/latex]\r\n\r\nA difference of cubes:\u00a0[latex]{a}^{3}-{b}^{3}[\/latex]\r\n\r\nIn this lesson you will see\u00a0you can factor each of these types of polynomials following a specific pattern. You will also learn how to factor polynomials that have negative or fractional exponents.","rendered":"<h3>Why Learn How to Factor Special Cases?<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2786 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/19191115\/Screen-Shot-2016-07-19-at-12.10.30-PM-300x153.png\" alt=\"Repeated pattern of interlocking plus signs, each row a different color following the rainbow spectrum.\" width=\"300\" height=\"153\" \/><\/p>\n<p>Some people like to find patterns in the world around them, like a game. There are some polynomials that, when factored, follow a specific pattern.<\/p>\n<p>These include:<\/p>\n<p>Perfect square trinomials of the form:\u00a0[latex]{a}^{2}+2ab+{b}^{2}[\/latex]<\/p>\n<p>A difference of squares:\u00a0[latex]{a}^{2}-{b}^{2}[\/latex]<\/p>\n<p>A sum of cubes:\u00a0[latex]{a}^{3}+{b}^{3}[\/latex]<\/p>\n<p>A difference of cubes:\u00a0[latex]{a}^{3}-{b}^{3}[\/latex]<\/p>\n<p>In this lesson you will see\u00a0you can factor each of these types of polynomials following a specific pattern. You will also learn how to factor polynomials that have negative or fractional exponents.<\/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-16324\">\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":13,"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":"933680a871454fc6912430bf6e5dd586","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-16324","chapter","type-chapter","status-publish","hentry"],"part":16188,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16324","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/169554"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16324\/revisions"}],"predecessor-version":[{"id":19031,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16324\/revisions\/19031"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/16188"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/16324\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=16324"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=16324"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=16324"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=16324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}