Polynomial Forms over Field form Principal Ideal Domain/Corollary 2

Theorem
Let $\left({F, +, \circ}\right)$ be a field whose zero is $0_F$ and whose unity is $1_F$.

Let $X$ be transcendental over $F$.

Let $F \left[{X}\right]$ be the ring of polynomials in $X$ over $F$.

Then $\left({f}\right)$ is a maximal ideal of $F \left[{X}\right]$ iff $\left({f}\right)$ is irreducible.