Let $k$ be a field, $f(x)\in k[x]$ be an irreducible polynomial over $k$, and $\alpha$ be a root of $f$. If $L$ is a field extension to $k$, what does $k(\alpha)\otimes_k L$ isomorphic to?
I'm trying to use the fact that $k(\alpha)\otimes_k L$ isomorphic to $k[x]/(f(x))\otimes_k L$ to drive some formulas, but I get struck at the beginning. Any help?