{"id":237015,"date":"2025-06-16T18:17:51","date_gmt":"2025-06-16T18:17:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237015"},"modified":"2025-06-16T18:17:53","modified_gmt":"2025-06-16T18:17:53","slug":"which-of-the-binomials-below-is-a-factor-of-this-trinomial","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/which-of-the-binomials-below-is-a-factor-of-this-trinomial\/","title":{"rendered":"Which of the binomials below is a factor of this trinomial"},"content":{"rendered":"\n<p>Which of the binomials below is a factor of this trinomial? x2 &#8211; 5x + 4<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To factor the trinomial:<\/p>\n\n\n\n<p><strong>x2\u22125x+4x^2 &#8211; 5x + 4&#215;2\u22125x+4<\/strong><\/p>\n\n\n\n<p>We are looking for <strong>two binomials<\/strong> of the form:(x\u2212a)(x\u2212b)(x &#8211; a)(x &#8211; b)(x\u2212a)(x\u2212b)<\/p>\n\n\n\n<p>such that when multiplied:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a+b=5a + b = 5a+b=5<\/li>\n\n\n\n<li>ab=4ab = 4ab=4<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify two numbers<\/h3>\n\n\n\n<p>We need two numbers that <strong>add to 5<\/strong> and <strong>multiply to 4<\/strong>. However, since the middle term is <strong>-5x<\/strong>, we are actually looking for two numbers that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>add to -5<\/strong><\/li>\n\n\n\n<li><strong>multiply to +4<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Try possible factor pairs of 4:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22121-1\u22121 and \u22124-4\u22124: \u22121+(\u22124)=\u22125-1 + (-4) = -5\u22121+(\u22124)=\u22125, \u22121\u00d7\u22124=4-1 \\times -4 = 4\u22121\u00d7\u22124=4<\/li>\n<\/ul>\n\n\n\n<p>Perfect match.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Write in factored form<\/h3>\n\n\n\n<p>x2\u22125x+4=(x\u22121)(x\u22124)x^2 &#8211; 5x + 4 = (x &#8211; 1)(x &#8211; 4)x2\u22125x+4=(x\u22121)(x\u22124)<\/p>\n\n\n\n<p>So, the binomials that are factors of the trinomial are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x\u22121)(x &#8211; 1)(x\u22121)<\/li>\n\n\n\n<li>(x\u22124)(x &#8211; 4)(x\u22124)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>One binomial factor of x2\u22125x+4x^2 &#8211; 5x + 4&#215;2\u22125x+4 is: (x\u22121)\\boxed{(x &#8211; 1)}(x\u22121)\u200b<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Factoring a trinomial involves breaking it into the product of two binomials. The standard form is:x2+bx+cx^2 + bx + cx2+bx+c<\/p>\n\n\n\n<p>To factor it, find two numbers whose <strong>sum is b<\/strong> and <strong>product is c<\/strong>. In this case, b=\u22125b = -5b=\u22125, c=4c = 4c=4. The numbers \u22121-1\u22121 and \u22124-4\u22124 meet these conditions. When you expand (x\u22121)(x\u22124)(x &#8211; 1)(x &#8211; 4)(x\u22121)(x\u22124) using the FOIL method:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First: x\u00d7x=x2x \\times x = x^2x\u00d7x=x2<\/li>\n\n\n\n<li>Outer: x\u00d7\u22124=\u22124xx \\times -4 = -4xx\u00d7\u22124=\u22124x<\/li>\n\n\n\n<li>Inner: \u22121\u00d7x=\u22121x-1 \\times x = -1x\u22121\u00d7x=\u22121x<\/li>\n\n\n\n<li>Last: \u22121\u00d7\u22124=4-1 \\times -4 = 4\u22121\u00d7\u22124=4<\/li>\n<\/ul>\n\n\n\n<p>Adding these: x2\u22124x\u2212x+4=x2\u22125x+4x^2 &#8211; 4x &#8211; x + 4 = x^2 &#8211; 5x + 4&#215;2\u22124x\u2212x+4=x2\u22125x+4<\/p>\n\n\n\n<p>So the factorization is correct. Therefore, (x\u22121)(x &#8211; 1)(x\u22121) is one of the binomial factors.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-784.jpeg\" alt=\"\" class=\"wp-image-237016\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which of the binomials below is a factor of this trinomial? x2 &#8211; 5x + 4 The Correct Answer and Explanation is: To factor the trinomial: x2\u22125x+4x^2 &#8211; 5x + 4&#215;2\u22125x+4 We are looking for two binomials of the form:(x\u2212a)(x\u2212b)(x &#8211; a)(x &#8211; b)(x\u2212a)(x\u2212b) such that when multiplied: Step 1: Identify two numbers We need [&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-237015","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237015","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=237015"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237015\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}