Question

f(x)=x^3+x^2-5x+2, g(x)=x^4-2x^3-x+2. Express the gcd(f(x),g(x)) as a combination of f(x) and g(x). I know the gcd is x-2, how do I write x-2 as a combination of f(x) and g(x)? Euclid's algorithm plays a role in this...