Let F be a field and let f ∈ F[X] be a polynomial with a splitting field E over F.
Show that for any element α of some extension of F, E(α) is a splitting field of f over F(α)
I'm not really sure how to begin with this question. I was thinking of working with f as a irreducible polynomial, or using α as a root of f, but wasn't sure how to proceed with the problem.
Any suggestions would be appreciated.