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Find the greatest common divisor of the given polynomials over the given field. Then write the...

Find the greatest common divisor of the given polynomials over the given field. Then write the greatest common divisor as a linear combination of the given polynomials. That is, given f(x) and g(x), find a(x) and b(x) so that d(x) = a(x)f(x) + b(x)g(x), where d(x) is the greatest common divisor of f(x) and g(x).

(a) x^10 − x^7 − x^5 + x^3 + x^2 − 1 and x^8 − x^5 − x^3 + 1 over Q.

(b) x^5 + x^4 + 2x^2 − x − 1 and x^3 + x^2 − x over Q.

(c) x^3 − 2x^2 + 3x + 1 and x^3 + 2x + 1 over Z5.

(d) x^5 + x^4 + 2x^2 + 4x + 4 and x^3 + x^2 + 4x over Z5

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