Degree of a field extension $F[x]/(g(x))$ over the field $F$

Question

Let $F$ be a field and let $F[x]$ be the ring of polynomials in $x$ over $F$. Let $g(x)$, of degree $n$, be in $F[x]$ and let $V=(g(x))$ be the ideal generated by $g(x)$ in $F[x]$. I have to prove that $F[x]/V$ is an $n$-dimensional vector space over $F$. Help me with the proof.