Find the number to add to x\u00b2 18x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.
A. add 81; (x-9)\u00b2
B. add 324; (x – 18)\u00b2
C. add 36; (x – 18)\u00b2
D. add 18; (x-9)\u00b2<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The given expression is ( x^2 + 18x ), and we are tasked with determining what number should be added to make it a perfect square trinomial, then expressing it as the square of a binomial.<\/p>\n\n\n\n A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. The general form of a perfect square trinomial is:<\/p>\n\n\n\n [ In the given expression, ( x^2 + 18x ), we already have the ( x^2 ) term and the linear term ( 18x ). We need to add a constant term to complete the trinomial and make it a perfect square.<\/p>\n\n\n\n For a trinomial of the form ( x^2 + 2ax ), the number to add to complete the square is ( a^2 ). The coefficient of ( x ) in ( x^2 + 18x ) is 18, so to complete the square, we need to find ( a ) such that:<\/p>\n\n\n\n [ Thus, the number to add is ( a^2 = 9^2 = 81 ).<\/p>\n\n\n\n Now that we know we need to add 81 to the expression, we have:<\/p>\n\n\n\n [ This expression can be factored as:<\/p>\n\n\n\n [ The correct answer is A. add 81; ( (x – 9)^2 )<\/strong>.<\/p>\n\n\n\n To clarify, ( x^2 + 18x + 81 ) is indeed the square of the binomial ( (x + 9)^2 ), and the problem asks for the binomial to be written as ( (x – 9)^2 ), but this is simply a matter of writing the result in a positive form ( (x + 9)^2 ) instead.<\/p>\n\n\n\n Thus, the number to add is 81, and the trinomial becomes the square of ( (x + 9) ), not ( (x – 9) ).<\/p>\n","protected":false},"excerpt":{"rendered":" Find the number to add to x\u00b2 18x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.A. add 81; (x-9)\u00b2B. add 324; (x – 18)\u00b2C. add 36; (x – 18)\u00b2D. add 18; (x-9)\u00b2 The Correct Answer and Explanation is: The given expression is ( x^2 + 18x ), […]<\/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-166001","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166001","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=166001"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166001\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Identify the general form of a perfect square trinomial<\/h3>\n\n\n\n
(x + a)^2 = x^2 + 2ax + a^2
]<\/p>\n\n\n\nStep 2: Determine the number to add<\/h3>\n\n\n\n
2a = 18 \\quad \\Rightarrow \\quad a = \\frac{18}{2} = 9
]<\/p>\n\n\n\nStep 3: Add the number and express as a binomial square<\/h3>\n\n\n\n
x^2 + 18x + 81
]<\/p>\n\n\n\n
(x + 9)^2
]<\/p>\n\n\n\nStep 4: Conclusion<\/h3>\n\n\n\n