I've recently been looking at the relationships between divisibility of polynomials and their degrees. This following idea has eluded me for a while.

Suppose and are polynomials in for a field, with irreducible. If is another irreducible polynomial that divides , then how can you conclude that the degree of divides the degree of ?

I know if has degree and has degree then has degree , I'm not sure if that immediately relates to the degree of . Thanks.