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Thread: [SOLVED] Dividing Polymonials by Polynomials

  1. #1
    Taelord
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    [SOLVED] Dividing Polymonials by Polynomials

    I am stuck with these. No idea how to do them. Here is my first problem:

    x^3+x^2y+xy^2+y^3 / x+y

    I don't want an answer. I want an explanation on how to do it.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Taelord View Post
    I am stuck with these. No idea how to do them. Here is my first problem:

    x^3+x^2y+xy^2+y^3 / x+y

    I don't want an answer. I want an explanation on how to do it.
    You can do it by long division, or you could simply note:
    $\displaystyle x^3+x^2y+xy^2+y^3 $

    $\displaystyle = (x^3 + x^2y) + (xy^2 + y^3)$

    $\displaystyle = x^2(x + y) + y^2(x + y)$

    $\displaystyle = (x^2 + y^2)(x + y)$

    Thus
    $\displaystyle \frac{x^3+x^2y+xy^2+y^3}{x + y} = x^2 + y^2$

    Since this is a division of a linear polynomial in x you could also rig a synthetic division for it.

    -Dan
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