{"id":255767,"date":"2025-07-13T08:53:17","date_gmt":"2025-07-13T08:53:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=255767"},"modified":"2025-07-13T08:53:20","modified_gmt":"2025-07-13T08:53:20","slug":"complete","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/13\/complete\/","title":{"rendered":"Complete"},"content":{"rendered":"\n

Please help me solve this!!! Vumc Polynomials (Answer ID # 02562741 Complete. huna”f eacne VcccD SedHelper; Date (24x^4 + 12x^3 + 8x^2) (4x) (-8x^4 + 72x^2) (AA4x) (4x + 16r` + 144x^2 + 576x) (Ax)y 74261 21ls (3x^2 + 6x^3 + 192x^2 + (6x^3 + 24x^2 + 96x + 384) 384x) (-3x) (-3x^4 + 12x^3 + (2Ix^3 + 21x) 192x^2 + (-21) 7681) (-x) (-12x+ (-12x^4 + 48x^2) [452x^2) (-3x) I1_ 10 (-2x^4 + 16x^8 + (40x+ + 256x^3 + 2x^2 + [6x) (-Zx) 164x^2 + 28x) 13 . (4x) (Ix^4 – 187x^2 + 792) (6x! + 24x^2) (11) (-3x) 15 . (28x’ + 196x? _ 336x 2352) + (28) (-4xt +32x^2) (-2x) 16 . (4x^4 – 58x^3 + [90x^2 + 17 72x) (2x) (ISx^5 + 6x^4 177x^3 72x^2 36x) (-3x) 18 (2x+ 72x^2) 19. (4x^5 160x^2 + 576x) (4x) 20 . (0) (2x) 121. (3x^5 + 189x^3 192x) (3x) 22 (Zx 2x^2) (~Zx) 23 (-8x^2 _ 48x^2 + 208x 160) (-8) 24 6x^3 12x^2 + 72x) 25. (-12x^4 + 144x^3 _ 24x^2) (3x) 26 . (-Sx^2 12x’ + 12x^2 + 48x^2 + 32x) (X) 27. 77x^3 324x) 28 (4x^4+ 576x^2) (-4x) 29 (-3x^5 + 6x^4 9x^2 – 12x^2 + 30x) (-3x) 30 (40x^5 + 44x^4 _ 408x^3 396x^2 + 432x) (4x)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Of course. Here is the solution to the polynomial division problems on the worksheet, along with a detailed explanation of the process.<\/p>\n\n\n\n

Explanation of the Method<\/h3>\n\n\n\n

This worksheet involves dividing a polynomial (an expression with multiple terms) by a monomial (an expression with a single term). The fundamental rule for this operation is straightforward: you must divide each individual term of the polynomial by the monomial divisor.<\/p>\n\n\n\n

This process involves two main steps for each term:<\/p>\n\n\n\n

    \n
  1. Divide the Coefficients:<\/strong>\u00a0Divide the number part of the term in the polynomial by the number part of the monomial. Pay close attention to the signs; for example, a negative number divided by a negative number results in a positive number.<\/li>\n\n\n\n
  2. Divide the Variables:<\/strong>\u00a0Divide the variable parts using the rules of exponents. When dividing variables with the same base, you subtract the exponents. For instance, x\u2075 \u00f7 x\u00b2 = x^(5-2) = x\u00b3. Remember that a variable with no visible exponent, like x, is considered to have an exponent of 1 (x\u00b9).<\/li>\n<\/ol>\n\n\n\n

    Let’s walk through a few examples from your worksheet.<\/p>\n\n\n\n

    Example: Problem 1<\/strong>
    (24x\u2074 – 12x\u00b3 – 8x\u00b2) \u00f7 (-4x)<\/strong><\/p>\n\n\n\n

    We divide each term by -4x:<\/p>\n\n\n\n

      \n
    • First term: (24x\u2074) \u00f7 (-4x). Divide the coefficients: 24 \u00f7 (-4) = -6. Divide the variables: x\u2074 \u00f7 x\u00b9 = x\u00b3. The result is\u00a0-6x\u00b3<\/strong>.<\/li>\n\n\n\n
    • Second term: (-12x\u00b3) \u00f7 (-4x). Divide the coefficients: -12 \u00f7 (-4) = +3. Divide the variables: x\u00b3 \u00f7 x\u00b9 = x\u00b2. The result is\u00a0+3x\u00b2<\/strong>.<\/li>\n\n\n\n
    • Third term: (-8x\u00b2) \u00f7 (-4x). Divide the coefficients: -8 \u00f7 (-4) = +2. Divide the variables: x\u00b2 \u00f7 x\u00b9 = x\u00b9. The result is\u00a0+2x<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Combining these results gives the final answer: -6x\u00b3 + 3x\u00b2 + 2x<\/strong>.<\/p>\n\n\n\n

      Example: Problem 23<\/strong>
      (-8x\u00b3 – 48x\u00b2 + 208x – 160) \u00f7 (-8)<\/strong><\/p>\n\n\n\n

      Here, the divisor is just a constant. The principle remains the same.<\/p>\n\n\n\n

        \n
      • (-8x\u00b3) \u00f7 (-8) =\u00a0x\u00b3<\/strong><\/li>\n\n\n\n
      • (-48x\u00b2) \u00f7 (-8) =\u00a0+6x\u00b2<\/strong><\/li>\n\n\n\n
      • (208x) \u00f7 (-8) =\u00a0-26x<\/strong><\/li>\n\n\n\n
      • (-160) \u00f7 (-8) =\u00a0+20<\/strong><\/li>\n<\/ul>\n\n\n\n

        The final answer is: x\u00b3 + 6x\u00b2 – 26x + 20<\/strong>.<\/p>\n\n\n\n

        Correct Answers<\/h3>\n\n\n\n

        Here are the complete answers for all the problems on the worksheet.<\/p>\n\n\n\n

          \n
        1. -6x\u00b3 + 3x\u00b2 + 2x<\/li>\n\n\n\n
        2. x\u00b3 + 4x\u00b2 – 36x – 144<\/li>\n\n\n\n
        3. 2x\u00b3 + 18x<\/li>\n\n\n\n
        4. x\u00b3 + 4x\u00b2 + 16x + 64<\/li>\n\n\n\n
        5. x\u00b3 – 2x\u00b2 – 64x + 128<\/li>\n\n\n\n
        6. -x\u00b2 – 1<\/li>\n\n\n\n
        7. x\u00b3 – 4x\u00b2 – 64x – 256<\/li>\n\n\n\n
        8. 3x\u00b3 + 363x<\/li>\n\n\n\n
        9. 4x\u00b3 – 16x<\/li>\n\n\n\n
        10. x\u00b3 – 8x\u00b2 + x – 8<\/li>\n\n\n\n
        11. -10x\u00b3 + 64x\u00b2 + 41x + 7<\/li>\n\n\n\n
        12. x\u00b3 – 17x + 72<\/li>\n\n\n\n
        13. -2x\u00b3 – 8x<\/li>\n\n\n\n
        14. x\u00b3 + 7x\u00b2 – 12x – 84<\/li>\n\n\n\n
        15. 2x\u00b3 – 16x<\/li>\n\n\n\n
        16. 2x\u00b3 – 29x\u00b2 + 95x + 36<\/li>\n\n\n\n
        17. -5x\u2074 – 2x\u00b3 + 59x\u00b2 + 24x + 12<\/li>\n\n\n\n
        18. 2x\u00b3 + 72x<\/li>\n\n\n\n
        19. x\u2074 – 40x\u00b2 + 144<\/li>\n\n\n\n
        20. 0<\/li>\n\n\n\n
        21. x\u2074 + 63x\u00b2 – 64<\/li>\n\n\n\n
        22. -x\u00b3 – x<\/li>\n\n\n\n
        23. x\u00b3 + 6x\u00b2 – 26x + 20<\/li>\n\n\n\n
        24. x\u00b3 – 6x\u00b2 – 12x + 72<\/li>\n\n\n\n
        25. -4x\u00b3 + 48x\u00b2 – 8x<\/li>\n\n\n\n
        26. -5x\u2074 – 12x\u00b3 + 12x\u00b2 + 48x + 32<\/li>\n\n\n\n
        27. x\u2074 + 77x\u00b2 – 324<\/li>\n\n\n\n
        28. -x\u00b3 – 144x<\/li>\n\n\n\n
        29. x\u2074 – 2x\u00b3 + 3x\u00b2 + 4x – 10<\/li>\n\n\n\n
        30. 10x\u2074 + 11x\u00b3 – 102x\u00b2 – 99x + 108<\/li>\n<\/ol>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Please help me solve this!!! Vumc Polynomials (Answer ID # 02562741 Complete. huna”f eacne VcccD SedHelper; Date (24x^4 + 12x^3 + 8x^2) (4x) (-8x^4 + 72x^2) (AA4x) (4x + 16r` + 144x^2 + 576x) (Ax)y 74261 21ls (3x^2 + 6x^3 + 192x^2 + (6x^3 + 24x^2 + 96x + 384) 384x) (-3x) (-3x^4 + 12x^3 […]<\/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-255767","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255767","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=255767"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255767\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255767"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255767"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255767"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}