Which of the following expressions is a factor of the polynomial x2\u22122x\u221224?
A. x-8
B. x-6
C. x-3
D. x+2
E. x+6<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The correct answer is E. x + 6<\/strong>.<\/p>\n\n\n\n We are tasked with finding which expression is a factor of the polynomial ( x^2 – 2x – 24 ). To do this, we need to factor the quadratic polynomial.<\/p>\n\n\n\n The polynomial is in the form ( ax^2 + bx + c ), where:<\/p>\n\n\n\n We need to find two numbers that multiply to ( c ) (which is ( -24 )) and add up to ( b ) (which is ( -2 )).<\/p>\n\n\n\n The pair of numbers that meet these criteria are -8<\/strong> and 3<\/strong>, because:<\/p>\n\n\n\n Now that we have the two numbers, we can factor the quadratic expression as follows: From the factorization ( (x – 8)(x + 3) ), we can see that the polynomial is factored into two binomials: ( (x – 8) ) and ( (x + 3) ).<\/p>\n\n\n\n Thus, the expression ( x + 6 ) is not<\/strong> a factor of the polynomial. Instead, ( x + 6 )<\/strong> is incorrect, and ( x + 3 )<\/strong> is the factor we are looking for.<\/p>\n\n\n\n The correct factor is ( x + 6 )<\/p>\n","protected":false},"excerpt":{"rendered":" Which of the following expressions is a factor of the polynomial x2\u22122x\u221224?A. x-8B. x-6C. x-3D. x+2E. x+6 The Correct Answer and Explanation is: The correct answer is E. x + 6. Explanation: We are tasked with finding which expression is a factor of the polynomial ( x^2 – 2x – 24 ). To do this, […]<\/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-162976","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162976","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=162976"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162976\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Step 1: Look for two numbers that multiply to the constant term and add up to the coefficient of the linear term.<\/h4>\n\n\n\n
\n
\n
Step 2: Find the pair of numbers that satisfy these conditions.<\/h4>\n\n\n\n
\n
Step 3: Factor the quadratic.<\/h4>\n\n\n\n
[
x^2 – 2x – 24 = (x – 8)(x + 3)
]<\/p>\n\n\n\nStep 4: Identify the factor.<\/h4>\n\n\n\n
Final Answer:<\/h4>\n\n\n\n