Which statement is true about the polynomial
\u201310m4n3 + 8m2n6 + 3m4n3 \u2013 2m2n6 \u2013 6m2n6 after it has been fully simplified?<\/p>\n\n\n\n
A It is a monomial with a degree of 4.
B It is a monomial with a degree of 7.
C It is a binomial with a degree of 6.
D It is a binomial with a degree of 8.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: B It is a monomial with a degree of 7<\/strong><\/mark><\/p>\n\n\n\n To simplify the polynomial (-10m^4n^3 + 8m^2n^6 + 3m^4n^3 – 2m^2n^6 – 6m^2n^6), we first need to combine like terms. Like terms are those that have the same variables raised to the same powers.<\/p>\n\n\n\n In summary, after fully simplifying the given polynomial, it reduces to a single monomial term, demonstrating the importance of recognizing and combining like terms in polynomial expressions.<\/p>\n","protected":false},"excerpt":{"rendered":" Which statement is true about the polynomial\u201310m4n3 + 8m2n6 + 3m4n3 \u2013 2m2n6 \u2013 6m2n6 after it has been fully simplified? A It is a monomial with a degree of 4.B It is a monomial with a degree of 7.C It is a binomial with a degree of 6.D It is a binomial with 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-156431","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156431","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=156431"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156431\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n
\n
\n
[
-10m^4n^3 + 3m^4n^3 = (-10 + 3)m^4n^3 = -7m^4n^3
]<\/li>\n\n\n\n
[
8m^2n^6 – 2m^2n^6 – 6m^2n^6 = (8 – 2 – 6)m^2n^6 = 0m^2n^6
]
Since the combined result is (0m^2n^6), these terms cancel out entirely.<\/li>\n<\/ul>\n\n\n\n\n
After simplifying, the polynomial becomes:
[
-7m^4n^3
]<\/li>\n\n\n\n
The simplified polynomial (-7m^4n^3) is a monomial because it consists of a single term. To find its degree, we add the exponents of the variables. Here, the degree is calculated as follows:<\/li>\n<\/ol>\n\n\n\n\n
[
\\text{Degree} = 4 + 3 = 7
]<\/li>\n<\/ul>\n\n\n\n\n
Based on the simplification, we have a monomial with a degree of (7). Therefore, the correct answer is B: It is a monomial with a degree of 7<\/strong>.<\/li>\n<\/ol>\n\n\n\n