An irreducible polynomial question 
Let $\mathbb F$ be a field and $f(x)$ an irreducible polynomial in $\mathbb F[x]$. Let $c$ be an element of $\mathbb F[x]/(f)$. Show that there exists $g \in \mathbb F[x]$, $g\neq 0$, such that $g(c)=0$.

We have to prove that $c$ is algebraic. I don't have any idea how to proceed.

Hint What can you say about the degree $$\left\lvert \frac{\mathbb F[x]}{\langle f(x) \rangle} : \mathbb F \right\rvert$$
