Let $f$ be an irreducible polynomial over $F$ and $K/F$ be a normal extension.
How to prove $f$ is factored by product of irreducible poly. over $K$ with same degree?
I tried to do it by if $f_1, f_2$ are two irreducible factors of $f$, then deg($f_1$)=deg($f_2$)
To do it, if $\alpha_i$ is a root of $f_i$, $F(\alpha_i)$ are isomorphic but how to extend it to $K(\alpha_i)$?