Let $F$ be a finite field, and $F[X]$ set of all polynomials in $F$, how to prove that: why all primitive polynomials $\;$ $f \in F[X]$ $\;$ must be an irreducible.
Note: Polynomial primitive is an irreductible polynomial over F, that have a root in the extension field of F and that's root is primive in the extension (Generator Element).