Polynomial Forms over Field form Principal Ideal Domain/Corollary 2

Corollary to Polynomial Forms over Field form Principal Ideal Domain
Let $\struct {F, +, \circ}$ be a field whose zero is $0_F$ and whose unity is $1_F$.

Let $X$ be transcendental over $F$.

Let $F \sqbrk X$ be the ring of polynomials in $X$ over $F$.

Let $f \in F \sqbrk X$.

Then $\ideal f$ is a maximal ideal of $F \sqbrk X$ $f$ is irreducible.