Let \(K\) be a field. A polynomial \(p\in K[x]\) is irreducible if \(p\) is nonconstant and there are no \(q,r\in K[x]\) with \(p=qr\), \(\deg q<\deg p\), and \(\deg r<\deg p\).
When is a polynomial irreducible, in terms of the degrees of its factors?