How to factor a trinomial when a is greater than 1<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Factoring a trinomial of the form ( ax^2 + bx + c ), where ( a > 1 ), can be done effectively by using the method of “splitting the middle term” or “trial and error.” Here\u2019s a step-by-step approach to factor such trinomials.<\/p>\n\n\n\n For the trinomial ( ax^2 + bx + c ), identify the coefficients ( a ), ( b ), and ( c ). For example, in the trinomial ( 6x^2 + 11x + 3 ), we have ( a = 6 ), ( b = 11 ), and ( c = 3 ).<\/p>\n\n\n\n Next, multiply ( a ) and ( c ). In our example, ( 6 \\times 3 = 18 ).<\/p>\n\n\n\n Now, we need to find two numbers that multiply to ( ac ) (in this case, 18) and add to ( b ) (in this case, 11). The numbers that work here are 9 and 2 since ( 9 \\times 2 = 18 ) and ( 9 + 2 = 11 ).<\/p>\n\n\n\n Use these two numbers to split the middle term ( bx ). Rewrite the trinomial as: Now, group the terms in pairs: Now, you can factor out the common binomial ( (2x + 3) ): Thus, the factored form of ( 6x^2 + 11x + 3 ) is ( (3x + 1)(2x + 3) ). This method of splitting the middle term is efficient for trinomials where ( a > 1 ), as it allows for systematic identification of factors while ensuring that the final answer maintains the original polynomial’s integrity.<\/p>\n","protected":false},"excerpt":{"rendered":" How to factor a trinomial when a is greater than 1 The correct Answer and Explanation is: Factoring a trinomial of the form ( ax^2 + bx + c ), where ( a > 1 ), can be done effectively by using the method of “splitting the middle term” or “trial and error.” Here\u2019s a […]<\/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-149643","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149643","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=149643"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149643\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Identify ( a ), ( b ), and ( c )<\/h3>\n\n\n\n
Step 2: Multiply ( a ) and ( c )<\/h3>\n\n\n\n
Step 3: Find two numbers that multiply to ( ac ) and add to ( b )<\/h3>\n\n\n\n
Step 4: Rewrite the trinomial<\/h3>\n\n\n\n
[
6x^2 + 9x + 2x + 3
]<\/p>\n\n\n\nStep 5: Factor by grouping<\/h3>\n\n\n\n
[
(6x^2 + 9x) + (2x + 3)
]
Factor out the greatest common factor from each group:
[
3x(2x + 3) + 1(2x + 3)
]<\/p>\n\n\n\nStep 6: Factor out the common binomial<\/h3>\n\n\n\n
[
(3x + 1)(2x + 3)
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n