1. The problem statement, all variables and given/known data Given that the minimal polynomial of a over rationals is x^4+x+8, find the minimal polynomial for 1/a over Q. 2. Relevant equations I know there is a lot of work done out there for finding the min. polynomials of a^k for k>0, however I've never seen anything with a^k for k<0. I have no intuition where to start with this problem, just wondering if there are methods out there.