Let char K = p 0 and let K[x] be irreducible of degree n.

Let char K = p ≠ 0 and let ∫ ϵ K[x] be irreducible of degree n. Let m be the largest nonnegative integer such that ∫ is a polynomial in x^Pm but is not a polynomial in x^pm+1. Then n = n_op^m. If u is a root of ∫, then [K(u) : K]_s = n_o and [K(u) : K]_i = p^m.