Let $f(x)=x^7-7x+3\in{Q[x]}$, show that $f(x)$ is irreducible over $Q$

Question

Let $f(x)=x^7-7x+3\in{Q[x]}$, show that $f(x)$ is irreducible over $Q$

I searched on internet and this polynomial is called Trinks' polynomial. I was trying to use Eisenstein's criterion to show it is irreducible, but it does not work.

Anyone can help me on this question?

Answer 1

Find the factorization of $f(x)$ over $\mathbb F_2$.