{"id":225524,"date":"2025-06-04T09:30:51","date_gmt":"2025-06-04T09:30:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225524"},"modified":"2025-06-04T09:30:54","modified_gmt":"2025-06-04T09:30:54","slug":"which-model-represents-the-factors-of-x2-9x-8-x-1-x-8","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-model-represents-the-factors-of-x2-9x-8-x-1-x-8\/","title":{"rendered":"Which model represents the factors of x^2 + 9x + 8? x + 1 x + 8"},"content":{"rendered":"\n<p>Which model represents the factors of x^2 + 9x + 8? x + 1 x + 8<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct factors of the quadratic expression x2+9x+8x^2 + 9x + 8 are: (x+1)(x+8)(x + 1)(x + 8)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>To factor the quadratic expression x2+9x+8x^2 + 9x + 8, we need to break it into two binomials of the form (x+a)(x+b)(x + a)(x + b), such that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>product<\/strong> of aa and bb is equal to the <strong>constant term<\/strong> 88,<\/li>\n\n\n\n<li>The <strong>sum<\/strong> of aa and bb is equal to the <strong>coefficient of the middle term<\/strong> 99.<\/li>\n<\/ul>\n\n\n\n<p>So we&#8217;re looking for two numbers that multiply to 8 and add up to 9.<\/p>\n\n\n\n<p>Let\u2019s list the factor pairs of 8:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00d78=81 \\times 8 = 8, and 1+8=91 + 8 = 9<\/li>\n\n\n\n<li>2\u00d74=82 \\times 4 = 8, but 2+4=62 + 4 = 6<\/li>\n<\/ul>\n\n\n\n<p>Among these, only <strong>1 and 8<\/strong> satisfy both conditions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00d78=81 \\times 8 = 8<\/li>\n\n\n\n<li>1+8=91 + 8 = 9<\/li>\n<\/ul>\n\n\n\n<p>This tells us the correct binomial factors are: (x+1)(x+8)(x + 1)(x + 8)<\/p>\n\n\n\n<p>Let\u2019s verify the factorization by expanding: (x+1)(x+8)=x2+8x+1x+8=x2+9x+8(x + 1)(x + 8) = x^2 + 8x + 1x + 8 = x^2 + 9x + 8<\/p>\n\n\n\n<p>The original expression x2+9x+8x^2 + 9x + 8 is recovered, confirming that the factorization is correct.<\/p>\n\n\n\n<p>This process uses <strong>factoring by inspection<\/strong>, a common method when the leading coefficient (the number in front of x2x^2) is 1. This approach involves finding two numbers whose product equals the constant term and whose sum equals the linear coefficient. It&#8217;s efficient and especially useful for simple trinomials like this one.<\/p>\n\n\n\n<p>Therefore, the expression x2+9x+8x^2 + 9x + 8 is correctly modeled by: (x+1)(x+8)(x + 1)(x + 8)<\/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-banner7-167.jpeg\" alt=\"\" class=\"wp-image-225525\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which model represents the factors of x^2 + 9x + 8? x + 1 x + 8 The Correct Answer and Explanation is: The correct factors of the quadratic expression x2+9x+8x^2 + 9x + 8 are: (x+1)(x+8)(x + 1)(x + 8) Explanation To factor the quadratic expression x2+9x+8x^2 + 9x + 8, we need to [&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-225524","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225524","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=225524"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225524\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}