# Math Help - Galois Theory

1. ## Galois Theory

Okay i have these two problems that can't solve so I decided to share:

1.-Let f(x) be an irreducible polynomial over F of degree n, and let K be a field extension of F with [K:F]=m. If gcd(n,m)=1 then f is irreducible over K

2.-Let K be a normal extension of F, and let f(x) be an irreducible polynomial over F (in F[x]). Let p, q be two monic irreducible factors of f in K. Prove that there is an h in Gal(K/F) such that h(p)=q. (h denotes both the F-automorphism of K and the natural induced homomorphism in K[x])

In the first one, I get that K has no root of K, and so f has no linear factors over K; but I can't see the general case.

In the second I tried building the splitting field of f over K, then since the elements of the Galois group permute the roots of f I try to translate that to K, but I get lost on how to proceed.