How to do the following problem?
Let $K$ be a normal extension of $F$, and let $f(x)\in F[x]$ be an irreducible polynomial over $F$. Let $g(x)$ and $p(x)$ be monic irreducible factors of $f(x)$ in $K[x]$. Prove that there is a $z\in\operatorname{Gal}(K/ F)$, with $z(g)=p$.