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Math Help - Remainder Theorem

  1. #1
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    Remainder Theorem

    Hi, Im having troubles in understanding how to solve these two equations and how to divide them.

    a) (2x^3 + 5x^2 - 2x - 3) / (x +1)

    b) (2x^3 - 7x^2 + 16x - 22) / (2x - 3)
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  2. #2
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    Hello,

    What do you mean by "solve these equations" ? With an equation comes a = sign, which is not here


    You can read this, this or this about polynomial long division (though the latter one is a more complicated example)
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  3. #3
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    Quote Originally Posted by flwer_13 View Post
    Hi, Im having troubles in understanding how to solve these two equations and how to divide them.

    a) (2x^3 + 5x^2 - 2x - 3) / (x +1)
    x alone divides into 2x^3 2x^2 times. Multiplying x+1 by 2x^2 gives 2x^3+ 2x^2:
    (2x^3+ 5x^2- 2x- 3)- (2x^3+ 2x^2)= 3x^2- 2x- 3.

    x alone divides into 3x^2 3x times. Multiplying x+1 by 3x gives 3x^2+ 3x:
    (3x^2- 2x- 3)- (3x^2+ 3x)= -5x- 3.

    x alone divides into -5x -5 times. Multiplying x+1 by -5 gives -5x- 5:
    (-5x-3)- (-5x-5)= 2.

    (2x^3 + 5x^2 - 2x - 3) / (x +1)= 2x^2+ 3x- 5 with remainder 2.

    b) (2x^3 - 7x^2 + 16x - 22) / (2x - 3)
    2x divides into 2x^3 x^2 times. Multiplying 2x-3 by x^2 gives 2x^3- 3x^3:
    (2x^3- 7x^2+ 16x- 22)- (2x^3- 3x^2)= -4x^2+ 16x- 22.

    Can you finish that one?
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