Let $F$ a field and $p(x)$ an irreducible polynomial in $F[x]$.
I'm trying to prove that $F[x]/(p(x))$ is an extension of $F$. I know there are two approaches. Either we can prove that $F$ is a subset of $F[x]/(p(x))$ (because $F[x]/(p(x))$ is a field) or we can show that there is an embedding between $F$ and $F[x]/(p(x))$.
I've tried the both cases, it seems to be easy, but I didn't get to solve it. Maybe because I'm a really beginner in this subject. I need help...