1. The problem statement, all variables and given/known data Let k be a field, and let f(x) = a_0 + a_1x +a_2x^2 +.......+a_nx^n in k[x] having degree n. If f(x) is irreducible, then so is a_n + a_n-1x+.....+a_0x^n 2. Relevant equations 3. The attempt at a solution A function that "reverses" the coefficients is not a well-defined function so it is necessary to use another approach. I'm wondering how this can be done, I'm pretty sure Eisenstein's Criterion isn't of much use here. Any help would be highly appreciated.