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Thread: Extended GCD algorithm for polynomials: write number 1/(a3+2a2+4), where a satisfies:

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    Extended GCD algorithm for polynomials: write number 1/(a3+2a2+4), where a satisfies:

    Hi,
    I am trying to solve a problem which asks to write number 1/(a3+2a2+4), where a satisfies: a4+2a3+2a2+8a = -2 without using other than rational numbers in the denominator. I came as far as reducing the problem to finding inverse of (x4+2x3+2x2+2s+2 + (f)) \in Q[x]/(f) (f) is here ideal generated by <a3+2a2+4>. Now I suppose I have to apply Extended Euclidean Algorithm for gcd(x4+2x3+2x2+2s+2, a3+2a2+4). However, I found out don't really know how to do the algorithm as I cannot get to Bezout's coefficients that are of degree <=3.
    I attach a photo of my progress. I would like somebody to point out where I fail in executing the algorithm correctly as I cannot find out.
    Thank you.

    photo: https://drive.google.com/open?id=1DR...EgUjALvQrSpPUz
    Last edited by missandtroop; 02-05-2018 at 11:46 PM.

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