Assistance and help on this would be great! thank you

Let F be a field. Let a(x), b(x) exist in F[x] be polynomials such that a(x)≠ 0 or b(x) ≠ 0.

Let d(x)=gcd(a(x), b(x), that is, d(x) is the monic polynomial in F[x] of highest degree such

that d(x)|a(x) and d(x)| b(x). Suppose that d1(x) exist in F[x] is a monic polynomial such that

d1(x)=a(x)u(x) + b(x)v(x) for some u(x), v(x) that exist in F[x], d1(x)| a(x) and d1(x)| b(x)

Prove that d(x) = d1(x).