Write the greatest common divisor over the given filed as alinear 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 + 1over 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.
I know the GCD's are
a. x^3-1 b. 1 c. 1 d.1
Please help me write them as a linear combination.
