{"id":883,"date":"2024-04-30T19:12:43","date_gmt":"2024-04-30T19:12:43","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=883"},"modified":"2024-11-25T17:06:38","modified_gmt":"2024-11-25T17:06:38","slug":"factoring-polynomials-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/factoring-polynomials-apply-it-1\/","title":{"raw":"Factoring Polynomials: Apply It 1","rendered":"Factoring Polynomials: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Factor polynomial expressions using the Greatest Common Factor (GCF) and by grouping to simplify expressions.<\/li>\r\n \t<li>Factor trinomials and perfect square trinomials into binomials.<\/li>\r\n \t<li>Break down expressions like differences of squares and cubic equations into their simpler factors.<\/li>\r\n \t<li>Use specific methods to factor expressions that contain fractional or negative exponents.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Mastering Advanced Factoring Techniques<\/strong><\/h2>\r\nLet's tackle some tricky expressions that really test your factoring skills! Whether you're dealing with polynomials that have higher degrees, unique coefficients, or require a mix of different factoring tricks, this section is all about leveling up your factoring game and getting you ready to solve real-world problems.\r\n\r\n<section class=\"textbox recall\">\r\n<ul>\r\n \t<li>Perfect Square Trinomials:<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {a}^{2}+2ab+{b}^{2}&amp; =&amp; {\\left(a+b\\right)}^{2}\\hfill \\\\ &amp; \\text{and}&amp; \\\\ \\hfill {a}^{2}-2ab+{b}^{2}&amp; =&amp; {\\left(a-b\\right)}^{2}\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<ul>\r\n \t<li>Difference of Squares:<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/p>\r\n\r\n<ul>\r\n \t<li>Sum of Two Cubes:<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]{a}^{3}+{b}^{3}=\\left(a+b\\right)\\left({a}^{2}-ab+{b}^{2}\\right)[\/latex]<\/p>\r\n\r\n<ul>\r\n \t<li>Difference of Two Cubes:<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex]{a}^{3}-{b}^{3}=\\left(a-b\\right)\\left({a}^{2}+ab+{b}^{2}\\right)[\/latex]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18891[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18892[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18893[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18894[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18895[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18896[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Factor polynomial expressions using the Greatest Common Factor (GCF) and by grouping to simplify expressions.<\/li>\n<li>Factor trinomials and perfect square trinomials into binomials.<\/li>\n<li>Break down expressions like differences of squares and cubic equations into their simpler factors.<\/li>\n<li>Use specific methods to factor expressions that contain fractional or negative exponents.<\/li>\n<\/ul>\n<\/section>\n<h2><strong>Mastering Advanced Factoring Techniques<\/strong><\/h2>\n<p>Let&#8217;s tackle some tricky expressions that really test your factoring skills! Whether you&#8217;re dealing with polynomials that have higher degrees, unique coefficients, or require a mix of different factoring tricks, this section is all about leveling up your factoring game and getting you ready to solve real-world problems.<\/p>\n<section class=\"textbox recall\">\n<ul>\n<li>Perfect Square Trinomials:<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill {a}^{2}+2ab+{b}^{2}& =& {\\left(a+b\\right)}^{2}\\hfill \\\\ & \\text{and}& \\\\ \\hfill {a}^{2}-2ab+{b}^{2}& =& {\\left(a-b\\right)}^{2}\\hfill \\end{array}[\/latex]<\/p>\n<ul>\n<li>Difference of Squares:<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/p>\n<ul>\n<li>Sum of Two Cubes:<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]{a}^{3}+{b}^{3}=\\left(a+b\\right)\\left({a}^{2}-ab+{b}^{2}\\right)[\/latex]<\/p>\n<ul>\n<li>Difference of Two Cubes:<\/li>\n<\/ul>\n<p style=\"text-align: center;\">[latex]{a}^{3}-{b}^{3}=\\left(a-b\\right)\\left({a}^{2}+ab+{b}^{2}\\right)[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18891\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18891&theme=lumen&iframe_resize_id=ohm18891&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18892\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18892&theme=lumen&iframe_resize_id=ohm18892&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18893\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18893&theme=lumen&iframe_resize_id=ohm18893&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18894\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18894&theme=lumen&iframe_resize_id=ohm18894&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18895\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18895&theme=lumen&iframe_resize_id=ohm18895&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18896\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18896&theme=lumen&iframe_resize_id=ohm18896&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":15,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":55,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/883"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/883\/revisions"}],"predecessor-version":[{"id":8073,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/883\/revisions\/8073"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/55"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/883\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=883"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=883"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=883"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}