1. The problem statement, all variables and given/known data Prove that f(x)=x^3-7x+11 is irreducible over Q 2. Relevant equations 3. The attempt at a solution I've tried using the eisenstein criterion for the polynomial. It doesn't work as it is written so I created a new polynomial g(x)=f(x+1)=(x+1)^3-7(x+1)+11=x^3+3x^2-4x+5. I did this because g(x) and f(x) are similar and if g(x) is irreducible so is f(x), but the new polynomial I constructed doesn't meet the eisenstein criterion either. Any ideas on where I should turn next?