{"id":183193,"date":"2025-01-16T05:07:38","date_gmt":"2025-01-16T05:07:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183193"},"modified":"2025-01-16T05:07:39","modified_gmt":"2025-01-16T05:07:39","slug":"w2-12w36","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/16\/w2-12w36\/","title":{"rendered":"w2-12w+36"},"content":{"rendered":"\n<p>Factor:<\/p>\n\n\n\n<p>w2-12w+36<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s factor the quadratic expression w2\u221212w+36w^2 &#8211; 12w + 36.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Recognize the structure<\/h3>\n\n\n\n<p>The quadratic expression is in the standard form: ax2+bx+cax^2 + bx + c<\/p>\n\n\n\n<p>In our case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1a = 1 (since the coefficient of w2w^2 is 1)<\/li>\n\n\n\n<li>b=\u221212b = -12<\/li>\n\n\n\n<li>c=36c = 36<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Factor the expression<\/h3>\n\n\n\n<p>We need to find two numbers that multiply to cc (36) and add up to bb (-12).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The factors of 36 are: 1,36;2,18;3,12;4,9;6,61, 36; 2, 18; 3, 12; 4, 9; 6, 6<\/li>\n\n\n\n<li>We need to check which pair of factors of 36 adds up to -12. The pair \u22126-6 and \u22126-6 works because: \u22126+(\u22126)=\u221212and\u22126\u00d7\u22126=36-6 + (-6) = -12 \\quad \\text{and} \\quad -6 \\times -6 = 36<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Rewrite the quadratic as a perfect square<\/h3>\n\n\n\n<p>Given that both numbers are \u22126-6, we can factor the expression as: w2\u221212w+36=(w\u22126)(w\u22126)w^2 &#8211; 12w + 36 = (w &#8211; 6)(w &#8211; 6)<\/p>\n\n\n\n<p>This is a perfect square trinomial, and it can be written as: (w\u22126)2(w &#8211; 6)^2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>w2\u221212w+36=(w\u22126)2w^2 &#8211; 12w + 36 = (w &#8211; 6)^2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The process involves identifying two numbers that multiply to the constant term (36) and add up to the coefficient of the linear term (-12). Once we find these numbers, we can rewrite the quadratic as the square of a binomial. In this case, the numbers are both \u22126-6, which simplifies the expression into a perfect square trinomial. Therefore, the factored form is (w\u22126)2(w &#8211; 6)^2, indicating that the original quadratic expression is the square of the binomial w\u22126w &#8211; 6. This method of factoring works efficiently for perfect square trinomials, where both the linear and constant terms are related by a consistent factor.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Factor: w2-12w+36 The Correct Answer and Explanation is : Let&#8217;s factor the quadratic expression w2\u221212w+36w^2 &#8211; 12w + 36. Step 1: Recognize the structure The quadratic expression is in the standard form: ax2+bx+cax^2 + bx + c In our case: Step 2: Factor the expression We need to find two numbers that multiply to cc [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-183193","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183193"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183193\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}