Let p be any prime number. Show that

1 + x + x^2/2! + x^3/3! ... + x^p/p! is irreducible over Q.

Okay for this one, I know that if the polynomial were degree 2 or 3 I could simply check whether it has roots, but I want to generalize to any prime p.

I would love to use Eisenstein Criterion, but because of the polynomial is not in Z[x] I cannot. I have spent a long time trying to convert the polynomial into a form that is usable. I came across an equation that said x^p -1/x-1 = 1+x+...+x^p-2+x^p-1. I have had no success so far.

I would really appreciate the help!