1. The problem statement, all variables and given/known data Let f in K[x] be a polynomial over a field K. Define the notion of a splitting field L of f over K. Show that if deg f = d, then f has a splitting field over K of degree dividing d! 3. The attempt at a solution If f is reducible, then this seems true by induction. I'm not sure about the case where f is irreducible over K though. Thanks for your help.