Factoring irreducible polynomial over normal extension

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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 $K(\alpha_i)$?