Polynomial Congurence Fields, I need help with this Theorem

Question

I need help with proving this Theorem:

Let $F$ be a field. let $a(x), m(x)$ be polynomials in $F[x]$ with $m(x)$ of positive degree. The congruence class $[a(x)]_{m(x)}$ is a unit in $F[x]_{m(x)}$ if and only if $gcd(a(x),m(x)) = 1$

I think that if $gcd(a(x),m(x)) = 1$ then m(x) is a irreducible, and thus $a(x)$ is a unit in $F[x]_{m(x)}$? is that true?? any help would be greatful.

thanks.