{"id":277041,"date":"2025-07-31T10:17:07","date_gmt":"2025-07-31T10:17:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=277041"},"modified":"2025-07-31T10:17:09","modified_gmt":"2025-07-31T10:17:09","slug":"factor-completely-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/factor-completely-2\/","title":{"rendered":"Factor completely"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct and complete factorization of the expression is (3q + 1)\u00b2<\/strong>.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

The problem requires us to factor the quadratic trinomial 9q\u00b2 + 6q + 1. Factoring is the process of breaking down a polynomial into a product of simpler expressions. In this case, we can identify the expression as a special type known as a perfect square trinomial.<\/p>\n\n\n\n

A perfect square trinomial has a specific structure: a\u00b2 + 2ab + b\u00b2 or a\u00b2 – 2ab + b\u00b2. The first form factors into (a + b)\u00b2, and the second factors into (a – b)\u00b2. We can check if our expression, 9q\u00b2 + 6q + 1, fits the first pattern.<\/p>\n\n\n\n

First, let’s examine the first term, 9q\u00b2. This term is a perfect square because the square root of 9 is 3 and the square root of q\u00b2 is q. Therefore, it can be written as (3q)\u00b2. This suggests that our ‘a’ term in the formula is 3q.<\/p>\n\n\n\n

Next, we examine the last term, 1. This is also a perfect square, as the square root of 1 is 1. It can be written as 1\u00b2. This suggests that our ‘b’ term in the formula is 1.<\/p>\n\n\n\n

The final step is to verify if the middle term, 6q, matches the ‘2ab’ part of the pattern. We can test this by multiplying 2 by our identified ‘a’ (3q) and ‘b’ (1). The calculation is 2 * (3q) * 1 = 6q. This result matches the middle term of the original expression exactly.<\/p>\n\n\n\n

Since all three parts of the expression fit the pattern a\u00b2 + 2ab + b\u00b2, we can conclude that 9q\u00b2 + 6q + 1 is a perfect square trinomial. The factored form is (a + b)\u00b2, which for our values becomes (3q + 1)\u00b2. This is the complete factorization because the binomial (3q + 1) cannot be factored further.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The correct and complete factorization of the expression is (3q + 1)\u00b2. Explanation The problem requires us to factor the quadratic trinomial 9q\u00b2 + 6q + 1. Factoring is the process of breaking down a polynomial into a product of simpler expressions. In this case, we can identify the expression […]<\/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-277041","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277041","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=277041"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/277041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=277041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=277041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=277041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}