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Math Help - Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials

  1. #1
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    Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials

    Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials of smaller degree with integer coefficients.
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  2. #2
    Super Member TheChaz's Avatar
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    Hint... input x^8 + 98x^4 + 1 at Wolfram|Alpha: Computational Knowledge Engine ... see below
    Last edited by TheChaz; March 18th 2011 at 03:38 AM. Reason: Too much spoon-feeding!
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by becz View Post
    Express x^8 + 98*(x^4)*(y^4) + y^8 as a product of two polynomials of smaller degree with integer coefficients.
    You know from symmetry the LHS has to factor as
    (x^4 + ax^3y + bx^2y^2 + cxy^3 + y^4)(x^4 + dx^3y + ex^2y^2 + fxy^3 + y^4)

    Multiplying this out and matching coefficients in the original will give you the factored equation's coefficients. (It took me two pages, but I got there in the end.)

    -Dan
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  4. #4
    Super Member TheChaz's Avatar
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    Rule 6.

    You have probably noticed that the expression to be factored has no x^7y term. This leads to the conclusion that (using the above factorization proposed by topsquark) a = -d. Similarly, we find that c = -f. This should simplify things, if only slightly.
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  5. #5
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    i get lost when i arrive at 2b = a^2 and 2b = c^2 . i know that a = -c but how can i prove that.

    Thanks
    Last edited by becz; March 20th 2011 at 01:31 PM.
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