How do I prove that this polynomial is irreducible? How do I prove that $x^4+1$ is an irreducible polynomial over $\mathbb Q$? I've already tried the Eisenstein criterion which gives to me any results to solve this question, I need help here.
Thanks

Try Eisenstein's test on $(x+1)^4+1=x^4+4x^3+6x^2+4x+2$. Can you pick the prime number?
Do convince yourself that (ir)reducibility is preserved by translations in the variable. Nifty trick.
