{"id":218564,"date":"2025-05-24T05:09:24","date_gmt":"2025-05-24T05:09:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218564"},"modified":"2025-05-24T05:09:26","modified_gmt":"2025-05-24T05:09:26","slug":"which-polynomial-represents-the-area-of-the-rectangle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/24\/which-polynomial-represents-the-area-of-the-rectangle\/","title":{"rendered":"Which polynomial represents the area of the rectangle"},"content":{"rendered":"\n

Which polynomial represents the area of the rectangle? Responses 4x^(2)-2x-6 4 x squared minus 2 x minus 6 4x^(2)-6 4 x squared minus 6 4x^(2)-10x-6 4 x squared minus 10 x minus 6 4x^(2)+2x-6 4 x squared plus 2 x minus 6 Rectangle with one side labeled four x minus six and another side labeled x plus one<\/p>\n\n\n\n

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

To find the polynomial that represents the area of a rectangle<\/strong>, we use the formula:<\/p>\n\n\n\n

$$
\\text{Area} = \\text{Length} \\times \\text{Width}
$$<\/p>\n\n\n\n

In this case, the rectangle has one side labeled $4x – 6$<\/strong> and the other side labeled $x + 1$<\/strong>. So we multiply these two expressions:<\/p>\n\n\n\n

$$
(4x – 6)(x + 1)
$$<\/p>\n\n\n\n

Now, apply the distributive property<\/strong> (also known as FOIL for binomials):<\/p>\n\n\n\n

$$
(4x – 6)(x + 1) = 4x(x + 1) – 6(x + 1)
$$<\/p>\n\n\n\n

Distribute each term:<\/p>\n\n\n\n

$$
4x(x + 1) = 4x^2 + 4x
$$<\/p>\n\n\n\n

$$
-6(x + 1) = -6x – 6
$$<\/p>\n\n\n\n

Now add the results together:<\/p>\n\n\n\n

$$
4x^2 + 4x – 6x – 6 = 4x^2 – 2x – 6
$$<\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

$$
\\boxed{4x^2 – 2x – 6}
$$<\/p>\n\n\n\n

\n\n\n\n

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

To determine the area of a rectangle when its sides are given as algebraic expressions, we multiply the two expressions. The two expressions provided are $4x – 6$ and $x + 1$. These expressions represent the length and the width of the rectangle.<\/p>\n\n\n\n

Multiplying binomials involves using the distributive property. This property tells us to multiply each term in the first expression by each term in the second.<\/p>\n\n\n\n

Step 1: Multiply the first term of the first binomial, $4x$, by each term of the second binomial:<\/p>\n\n\n\n

    \n
  • $4x \\cdot x = 4x^2$<\/li>\n\n\n\n
  • $4x \\cdot 1 = 4x$<\/li>\n<\/ul>\n\n\n\n

    Step 2: Multiply the second term of the first binomial, $-6$, by each term of the second binomial:<\/p>\n\n\n\n

      \n
    • $-6 \\cdot x = -6x$<\/li>\n\n\n\n
    • $-6 \\cdot 1 = -6$<\/li>\n<\/ul>\n\n\n\n

      Step 3: Combine all terms:<\/p>\n\n\n\n

        \n
      • $4x^2 + 4x – 6x – 6$<\/li>\n<\/ul>\n\n\n\n

        Step 4: Combine like terms:<\/p>\n\n\n\n

          \n
        • $4x^2 – 2x – 6$<\/li>\n<\/ul>\n\n\n\n

          This polynomial, $4x^2 – 2x – 6$, represents the total area of the rectangle in terms of $x$. It accounts for all the changes in the side lengths as $x$ changes and is derived using fundamental algebraic principles. Therefore, the correct response is $4x^2 – 2x – 6$<\/strong>.<\/p>\n\n\n\n

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

          Which polynomial represents the area of the rectangle? Responses 4x^(2)-2x-6 4 x squared minus 2 x minus 6 4x^(2)-6 4 x squared minus 6 4x^(2)-10x-6 4 x squared minus 10 x minus 6 4x^(2)+2x-6 4 x squared plus 2 x minus 6 Rectangle with one side labeled four x minus six and another side labeled […]<\/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-218564","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218564","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=218564"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218564\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}