{"id":2739,"date":"2025-08-13T18:33:54","date_gmt":"2025-08-13T18:33:54","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2739"},"modified":"2025-10-17T18:37:14","modified_gmt":"2025-10-17T18:37:14","slug":"trigonometric-identities-and-equations-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/trigonometric-identities-and-equations-background-youll-need-3\/","title":{"raw":"Trigonometric Identities and Equations: Background You'll Need 3","rendered":"Trigonometric Identities and Equations: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Solve quadratic equations by factoring<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox recall\" aria-label=\"Recall\">A quadratic equation can often be written as [latex]ax^2 + bx + c = 0[\/latex].\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p data-start=\"2918\" data-end=\"3025\">To solve by factoring:<\/p>\r\n\r\n<ol data-start=\"3027\" data-end=\"3189\">\r\n \t<li data-start=\"3027\" data-end=\"3087\">\r\n<p data-start=\"3030\" data-end=\"3087\">Rewrite the equation in standard form (set equal to 0).<\/p>\r\n<\/li>\r\n \t<li data-start=\"3088\" data-end=\"3125\">\r\n<p data-start=\"3091\" data-end=\"3125\">Factor the quadratic expression.<\/p>\r\n<\/li>\r\n \t<li data-start=\"3126\" data-end=\"3158\">\r\n<p data-start=\"3129\" data-end=\"3158\">Set each factor equal to 0.<\/p>\r\n<\/li>\r\n \t<li data-start=\"3159\" data-end=\"3189\">\r\n<p data-start=\"3162\" data-end=\"3189\">Solve for [latex]x[\/latex].<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<ol>\r\n \t<li>Solve [latex]x^2 + 5x + 6 = 0[\/latex].<\/li>\r\n \t<li>Solve [latex]2x^2 - 8x = 0[\/latex].<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"838421\"]Show Solutions[\/reveal-answer]\r\n[hidden-answer a=\"838421\"]\r\n<ol>\r\n \t<li>Solve [latex]x^2 + 5x + 6 = 0[\/latex].\r\n[latex]\r\n\\begin{align}\r\nx^2 + 5x + 6 &amp;= 0 \\\\\r\n(x + 2)(x + 3) &amp;= 0 \\\\\r\nx + 2 = 0 \\text{ or } x + 3 = 0 \\\\\r\nx &amp;= -2 \\text{ or } x = -3\r\n\\end{align}\r\n[\/latex]<\/li>\r\n \t<li>Solve [latex]2x^2 - 8x = 0[\/latex].\r\n<p data-start=\"3473\" data-end=\"3499\">First, factor out the GCF.<\/p>\r\n<p data-start=\"3501\" data-end=\"3653\">[latex]\r\n\\begin{align}\r\n2x^2 - 8x &amp;= 0 \\\\\r\n2x(x - 4) &amp;= 0 \\\\\r\n2x = 0 \\text{ or } (x - 4) = 0 \\\\\r\nx &amp;= 0 \\text{ or } x = 4\r\n\\end{align}\r\n[\/latex]<\/p>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313773[\/ohm_question]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313774[\/ohm_question]\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Solve quadratic equations by factoring<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\" aria-label=\"Recall\">A quadratic equation can often be written as [latex]ax^2 + bx + c = 0[\/latex].<\/p>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p data-start=\"2918\" data-end=\"3025\">To solve by factoring:<\/p>\n<ol data-start=\"3027\" data-end=\"3189\">\n<li data-start=\"3027\" data-end=\"3087\">\n<p data-start=\"3030\" data-end=\"3087\">Rewrite the equation in standard form (set equal to 0).<\/p>\n<\/li>\n<li data-start=\"3088\" data-end=\"3125\">\n<p data-start=\"3091\" data-end=\"3125\">Factor the quadratic expression.<\/p>\n<\/li>\n<li data-start=\"3126\" data-end=\"3158\">\n<p data-start=\"3129\" data-end=\"3158\">Set each factor equal to 0.<\/p>\n<\/li>\n<li data-start=\"3159\" data-end=\"3189\">\n<p data-start=\"3162\" data-end=\"3189\">Solve for [latex]x[\/latex].<\/p>\n<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<ol>\n<li>Solve [latex]x^2 + 5x + 6 = 0[\/latex].<\/li>\n<li>Solve [latex]2x^2 - 8x = 0[\/latex].<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q838421\">Show Solutions<\/button><\/p>\n<div id=\"q838421\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Solve [latex]x^2 + 5x + 6 = 0[\/latex].<br \/>\n[latex]\\begin{align}  x^2 + 5x + 6 &= 0 \\\\  (x + 2)(x + 3) &= 0 \\\\  x + 2 = 0 \\text{ or } x + 3 = 0 \\\\  x &= -2 \\text{ or } x = -3  \\end{align}[\/latex]<\/li>\n<li>Solve [latex]2x^2 - 8x = 0[\/latex].\n<p data-start=\"3473\" data-end=\"3499\">First, factor out the GCF.<\/p>\n<p data-start=\"3501\" data-end=\"3653\">[latex]\\begin{align}  2x^2 - 8x &= 0 \\\\  2x(x - 4) &= 0 \\\\  2x = 0 \\text{ or } (x - 4) = 0 \\\\  x &= 0 \\text{ or } x = 4  \\end{align}[\/latex]<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313773\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313773&theme=lumen&iframe_resize_id=ohm313773&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313774\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313774&theme=lumen&iframe_resize_id=ohm313774&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":67,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":201,"module-header":"background_you_need","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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2739"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2739\/revisions"}],"predecessor-version":[{"id":4720,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2739\/revisions\/4720"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/201"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2739\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2739"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2739"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2739"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}