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Math Help - dividing polynomials

  1. #1
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    dividing polynomials

    Again, from a guy at work...this question has me stumped:

    (4x^3+x+10) / (2x-1)

    The answer in the book is 2x^2+x+1+11/2x-1

    I for the life of me can not figure out how they are getting the +1+11/2x-1
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  2. #2
    Senior Member tukeywilliams's Avatar
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    They used the remainder. The remainder is  \frac{11}{2x-1} . Also  2x-1 goes into  2x+10 once. And thats how we get the remainder term.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Stuck686 View Post
    Again, from a guy at work...this question has me stumped:

    (4x^3+x+10) / (2x-1)

    The answer in the book is 2x^2+x+1+11/2x-1

    I for the life of me can not figure out how they are getting the +1+11/2x-1
    This is done by long division.
    \frac{4x^3 + x + 10}{2x - 1} = \frac{4x^3 + 0\cdot x^2 + x + 10}{2x - 1}

    I'm not going to write this out showing all the work, I'll just do it this way:
    \frac{4x^3 + 0\cdot x^2 + x + 10}{2x - 1}

    = \frac{(4x^3 - 2x^2) +  2x^2 + x + 10}{2x - 1} = \frac{4x^3 - 2x^2}{2x - 1} + \frac{2x^2 + x + 10}{2x - 1}

     = 2x^2 + \frac{2x^2 + x + 10}{2x - 1}

    = 2x^2 + \frac{(2x^2 - x) + x + x + 10}{2x - 1} = 2x^2 + \frac{2x^2 - x}{2x - 1} + \frac{2x + 10}{2x - 1}

    = 2x^2 + x + \frac{2x + 10}{2x - 1}

    = 2x^2 + x + \frac{(2x - 1) + 1 + 10}{2x - 1} = 2x^2 + x + \frac{2x - 1}{2x - 1} + \frac{11}{2x - 1}

    = 2x^2 + x + 1 + \frac{11}{2x - 1}

    -Dan
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  4. #4
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    Quote Originally Posted by Stuck686 View Post
    Again, from a guy at work...this question has me stumped:

    (4x^3+x+10) / (2x-1)

    The answer in the book is 2x^2+x+1+11/2x-1

    I for the life of me can not figure out how they are getting the +1+11/2x-1
    Hello,

    I assume that you know how to do synthetic division(?):
    Code:
                                                       11
    ( 4x + 0*x + x + 10)  (2x - 1) = 2x + x + 1 + ------
     ( 4x- 2x)                                       2x-1
    -----------                                                
            2x +  x
           (2x - x )
          -----------
                  2x + 10
                 (2x -  1)
                ---------
                        11
    You have to list all powers of x in the dividend.
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