{"id":235475,"date":"2025-06-15T11:56:26","date_gmt":"2025-06-15T11:56:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235475"},"modified":"2025-06-15T11:56:27","modified_gmt":"2025-06-15T11:56:27","slug":"if-4x-3-is-a-factor-of-8x2-14x-15-find-the-other-facto","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/if-4x-3-is-a-factor-of-8x2-14x-15-find-the-other-facto\/","title":{"rendered":"If 4x – 3 is a factor of 8x^2 + 14x – 15, find the other facto"},"content":{"rendered":"\n

If 4x – 3 is a factor of 8x^2 + 14x – 15, find the other factor?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
The other factor is 2x + 5<\/strong><\/p>\n\n\n\n

\n\n\n\n

Step-by-step Explanation (Without Using the Word “We”):<\/strong><\/p>\n\n\n\n

Given that 4x – 3<\/strong> is a factor of the quadratic expression:8×2+14x\u2212158x^2 + 14x – 158×2+14x\u221215<\/p>\n\n\n\n

The goal is to find the other factor.<\/p>\n\n\n\n

Start by assuming the product of two binomials equals the expression. Since one factor is already known:8×2+14x\u221215=(4x\u22123)(ax+b)8x^2 + 14x – 15 = (4x – 3)(ax + b)8×2+14x\u221215=(4x\u22123)(ax+b)<\/p>\n\n\n\n

To find the values of a<\/strong> and b<\/strong>, expand the right-hand side:(4x\u22123)(ax+b)=4ax2+(4b\u22123a)x\u22123b(4x – 3)(ax + b) = 4a x^2 + (4b – 3a)x – 3b(4x\u22123)(ax+b)=4ax2+(4b\u22123a)x\u22123b<\/p>\n\n\n\n

Now match this with the original quadratic:8×2+14x\u221215=4ax2+(4b\u22123a)x\u22123b8x^2 + 14x – 15 = 4a x^2 + (4b – 3a)x – 3b8x2+14x\u221215=4ax2+(4b\u22123a)x\u22123b<\/p>\n\n\n\n

Match the coefficients on both sides:<\/p>\n\n\n\n

    \n
  1. 4a=8\u21d2a=24a = 8 \\Rightarrow a = 24a=8\u21d2a=2<\/li>\n\n\n\n
  2. \u22123b=\u221215\u21d2b=5-3b = -15 \\Rightarrow b = 5\u22123b=\u221215\u21d2b=5<\/li>\n\n\n\n
  3. Verify middle term: 4b\u22123a=4(5)\u22123(2)=20\u22126=144b – 3a = 4(5) – 3(2) = 20 – 6 = 144b\u22123a=4(5)\u22123(2)=20\u22126=14<\/li>\n<\/ol>\n\n\n\n

    All terms match the original expression, confirming correctness.<\/p>\n\n\n\n

    Therefore, the full factorization of the quadratic is:8×2+14x\u221215=(4x\u22123)(2x+5)8x^2 + 14x – 15 = (4x – 3)(2x + 5)8×2+14x\u221215=(4x\u22123)(2x+5)<\/p>\n\n\n\n

    So, the other factor is:2x+5\\boxed{2x + 5}2x+5\u200b<\/p>\n\n\n\n

    Summary:<\/strong><\/p>\n\n\n\n

    The quadratic expression was factored using expansion and coefficient comparison. Since the known factor was 4x\u221234x – 34x\u22123, matching the resulting expression with the original quadratic led to determining the unknown binomial. All coefficients aligned perfectly, verifying the solution. Hence, 2x+52x + 52x+5 is the other factor.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    If 4x – 3 is a factor of 8x^2 + 14x – 15, find the other factor? The Correct Answer and Explanation is: Correct Answer:The other factor is 2x + 5 Step-by-step Explanation (Without Using the Word “We”): Given that 4x – 3 is a factor of the quadratic expression:8×2+14x\u2212158x^2 + 14x – 158×2+14x\u221215 The […]<\/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-235475","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235475","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=235475"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235475\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}