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Math Help - [SOLVED] Polynomial question

  1. #1
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    [SOLVED] Polynomial question

    Hi, this is probably quite a simple question, but i am stuck, and can't find anything like it in the lecture notes, so your help will be appreciated.

    the question is
    Write down the polynomial P in x,y such that that x^4 - x^4 = (x-y)P

    Explanations with answers will really help me too! Thanks
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  2. #2
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    Quote Originally Posted by Rapid_W View Post
    Hi, this is probably quite a simple question, but i am stuck, and can't find anything like it in the lecture notes, so your help will be appreciated.

    the question is
    Write down the polynomial P in x,y such that that x^4 - x^4 = (x-y)P

    Explanations with answers will really help me too! Thanks
    x^4-x^4 = 0 . Sure you didn't mean x^4-y^4?

    If so x^4-y^4 is the difference of two squares:

    x^4-y^4 = (x^2-y^2)(x^2+y^2)

    However, x^2-y^2 is also the difference of two squares

    x^4-y^4 = (x-y)(x+y)(x^2+y^2)

    which gives P = (x+y)(x^2+y^2) = x^3 + xy^2 + x^2y + y^3
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  3. #3
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    Yes, i did mean that sorry! Thanks very much for the answer
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