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Use the Euclidean algorithm for polynomials to find the gcd of each pair of polynomials, over the designated field F. Then write the gcd as s(x)f(x) +t(x)g(x) where s(x), t(x) ( F[x].
a) f(x) = x2 + x - 2, g(x) = x5 - x4 + x3 + x2 - x - 1 in Q[v]
b) f(x) = x4 + x3 + l, g(x) = x2 + x + lin Z2[x]
c) f(x) = x4 + 2x2 + 2x + 2, g(x) = 2x3 + 2x2 + x+ 1 in Z3[x] |
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