Reducible and irreducible polynomials

Let \(k\) be a field and let \(f\in k[x]\) be nonconstant. The polynomial \(f\) is reducible if there exist \(g, h\in k[x]\) with \(\deg g, \deg h \geq 1\) and \(f = gh\). The polynomial \(f\) is irreducible if it is not reducible.