{"id":258777,"date":"2025-07-18T12:35:46","date_gmt":"2025-07-18T12:35:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258777"},"modified":"2025-07-18T12:35:48","modified_gmt":"2025-07-18T12:35:48","slug":"y-1-4y%e2%81%b5-4y%c2%b3-y%c2%b2-4y-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/y-1-4y%e2%81%b5-4y%c2%b3-y%c2%b2-4y-3\/","title":{"rendered":"y + 1 ) 4y\u2075 \u2013 4y\u00b3 \u2013 y\u00b2 \u2013 4y \u2013 3"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct answer is 4y\u2074 \u2013 4y\u00b3 \u2013 y \u2013 3<\/strong>.<\/p>\n\n\n\n

This problem is solved using polynomial long division. The goal is to divide the dividend, 4y\u2075 \u2013 4y\u00b3 \u2013 y\u00b2 \u2013 4y \u2013 3, by the divisor, y + 1.<\/p>\n\n\n\n

First, we set up the division. It is crucial to account for all powers of the variable y in descending order in the dividend. The dividend is missing a term with y\u2074, so we insert a placeholder, 0y\u2074, to maintain proper column alignment. The dividend is written as 4y\u2075 + 0y\u2074 \u2013 4y\u00b3 \u2013 y\u00b2 \u2013 4y \u2013 3.<\/p>\n\n\n\n

The process begins by dividing the first term of the dividend, 4y\u2075, by the first term of the divisor, y. The result is 4y\u2074, which becomes the first term of our quotient. We then multiply this 4y\u2074 by the entire divisor (y + 1) to get 4y\u2075 + 4y\u2074. This result is placed below the dividend and subtracted. The subtraction (4y\u2075 + 0y\u2074) \u2013 (4y\u2075 + 4y\u2074) yields \u20134y\u2074. We then bring down the next term from the dividend, \u20134y\u00b3, to get a new expression: \u20134y\u2074 \u2013 4y\u00b3.<\/p>\n\n\n\n

Next, we repeat the process. We divide the first term of this new expression, \u20134y\u2074, by the first term of the divisor, y, which gives us \u20134y\u00b3. This is the second term of our quotient. Multiplying \u20134y\u00b3 by the divisor (y + 1) gives \u20134y\u2074 \u2013 4y\u00b3. Subtracting this from the current line, (\u20134y\u2074 \u2013 4y\u00b3) \u2013 (\u20134y\u2074 \u2013 4y\u00b3), results in 0. We then bring down the next two terms, \u2013y\u00b2 and \u20134y.<\/p>\n\n\n\n

Now, we divide \u2013y\u00b2 by y to get \u2013y, the third term of the quotient. Multiplying \u2013y by (y + 1) gives \u2013y\u00b2 \u2013 y. We subtract this from the current expression: (\u2013y\u00b2 \u2013 4y) \u2013 (\u2013y\u00b2 \u2013 y) results in \u20133y. We bring down the final term, \u20133.<\/p>\n\n\n\n

Finally, we divide \u20133y by y, which gives \u20133. This is the last term of our quotient. Multiplying \u20133 by (y + 1) gives \u20133y \u2013 3. Subtracting this from the remaining expression (\u20133y \u2013 3) results in a remainder of 0.<\/p>\n\n\n\n

Since the remainder is 0, the division is exact. The final quotient is the polynomial we constructed on top: 4y\u2074 \u2013 4y\u00b3 \u2013 y \u2013 3.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The correct answer is 4y\u2074 \u2013 4y\u00b3 \u2013 y \u2013 3. This problem is solved using polynomial long division. The goal is to divide the dividend, 4y\u2075 \u2013 4y\u00b3 \u2013 y\u00b2 \u2013 4y \u2013 3, by the divisor, y + 1. First, we set up the division. It is crucial […]<\/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-258777","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258777","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=258777"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258777\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}