The polynomial x3 + 8 is equal to<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The polynomial ( x^3 + 8 ) can be factored using the sum of cubes formula. The sum of cubes formula is:<\/p>\n\n\n\n [ In the given polynomial ( x^3 + 8 ), we can recognize this as a sum of cubes, since ( 8 ) is equal to ( 2^3 ). Therefore, we can rewrite the polynomial as:<\/p>\n\n\n\n [ Now, using the sum of cubes formula, where ( a = x ) and ( b = 2 ), we can factor the polynomial as:<\/p>\n\n\n\n [ Simplifying the second factor:<\/p>\n\n\n\n [ Thus, the factored form of ( x^3 + 8 ) is:<\/p>\n\n\n\n [ The sum of cubes formula helps in factoring polynomials of the form ( a^3 + b^3 ). This formula is based on the idea that any number that is the sum of two cubes can be expressed as the product of a binomial and a trinomial. The binomial ( (a + b) ) represents the sum of the cube roots, while the trinomial ( a^2 – ab + b^2 ) accounts for the other terms that arise when expanding the product.<\/p>\n\n\n\n In the case of ( x^3 + 8 ), we recognize that ( 8 ) is a perfect cube, ( 2^3 ), and apply the sum of cubes formula with ( a = x ) and ( b = 2 ). This allows us to factor the expression into the product of two terms: ( (x + 2) ) and ( (x^2 – 2x + 4) ).<\/p>\n\n\n\n This factoring method is very useful because it simplifies polynomials and makes them easier to solve or manipulate in algebraic problems. The factored form ( (x + 2)(x^2 – 2x + 4) ) can be used for further analysis, such as finding the roots or solving equations.<\/p>\n","protected":false},"excerpt":{"rendered":" The polynomial x3 + 8 is equal to The Correct Answer and Explanation is: The polynomial ( x^3 + 8 ) can be factored using the sum of cubes formula. The sum of cubes formula is: [a^3 + b^3 = (a + b)(a^2 – ab + b^2)] In the given polynomial ( x^3 + 8 […]<\/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-166660","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166660","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=166660"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166660\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166660"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
a^3 + b^3 = (a + b)(a^2 – ab + b^2)
]<\/p>\n\n\n\n
x^3 + 8 = x^3 + 2^3
]<\/p>\n\n\n\n
x^3 + 2^3 = (x + 2)(x^2 – 2x + 2^2)
]<\/p>\n\n\n\n
x^2 – 2x + 4
]<\/p>\n\n\n\n
x^3 + 8 = (x + 2)(x^2 – 2x + 4)
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n