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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/(a^{3}+2a^{2}+4), where a satisfies: a^{4}+2a^{3}+2a^{2}+8a = 2 without using other than rational numbers in the denominator. I came as far as reducing the problem to finding inverse of (x^{4}+2x^{3}+2x^{2}+2s+2 + (f)) \in Q[x]/(f) (f) is here ideal generated by <a^{3}+2a^{2}+4>. Now I suppose I have to apply Extended Euclidean Algorithm for gcd(x^{4}+2x^{3}+2x^{2}+2s+2, a^{3}+2a^{2}+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; 02052018 at 11:46 PM.
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