Show from Exercise 17 that an irreducible polynomial q(x) over a field F of characteristic p ≠ 0 is not separable if and only if each exponent of each term of q(x) is divisible by p.

Data from Exercise 17

Let ƒ(x) ∈ F[x], and let a ∈ F̅ be a zero of f(x) of multiplicity v. Show that v > 1 if and only if α is also a zero of f'(x).