What is the remainder when a\u00b3 – 4 is divided by a+2?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the remainder when ( a^3 – 4 ) is divided by ( a + 2 ), we can use synthetic division<\/strong> or polynomial division<\/strong>. Here\u2019s a step-by-step approach using synthetic division:<\/p>\n\n\n\n We want to divide ( a^3 – 4 ) by ( a + 2 ).<\/p>\n\n\n\n According to the Remainder Theorem<\/strong>, the remainder of a polynomial ( f(a) ) divided by ( a – c ) is given by ( f(c) ). In this case, we are dividing by ( a + 2 ), which means ( c = -2 ).<\/p>\n\n\n\n To find the remainder, we substitute ( a = -2 ) into the polynomial ( f(a) = a^3 – 4 ).<\/p>\n\n\n\n Now, calculate ( f(-2) ): Thus, the remainder when ( a^3 – 4 ) is divided by ( a + 2 ) is -12<\/strong>.<\/p>\n\n\n\n When dividing a polynomial by a linear factor like ( a + 2 ), the Remainder Theorem simplifies the process by allowing us to substitute ( a = -2 ) directly into the polynomial to find the remainder. Instead of performing long polynomial division or synthetic division, the Remainder Theorem gives us a quick shortcut.<\/p>\n\n\n\n In this case, we substituted ( a = -2 ) into ( f(a) = a^3 – 4 ) and found that the value of the polynomial at ( a = -2 ) is ( -12 ). This result is the remainder because the remainder theorem tells us that dividing a polynomial by ( a – c ) gives a remainder of ( f(c) ). Since we are dividing by ( a + 2 ), the remainder is ( f(-2) = -12 ).<\/p>\n\n\n\n Hence, the remainder is -12<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the remainder when a\u00b3 – 4 is divided by a+2? The Correct Answer and Explanation is : To find the remainder when ( a^3 – 4 ) is divided by ( a + 2 ), we can use synthetic division or polynomial division. Here\u2019s a step-by-step approach using synthetic division: Step 1: Set […]<\/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-152995","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152995","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=152995"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152995\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152995"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Set up the division<\/h3>\n\n\n\n
Step 2: Apply the Remainder Theorem<\/h3>\n\n\n\n
Step 3: Substitute ( a = -2 ) into the polynomial<\/h3>\n\n\n\n
[
f(-2) = (-2)^3 – 4 = -8 – 4 = -12
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n