Factorize $x^7-7x^6+21x^5-35x^4+35x^3-21x^2+20x+14$ into $\Bbb Q$-irreducible factors.
I've made the substitution $y=x-1$.
So I get $y^7+13y+28$ which satisfies Eisenstein's Criterion for $p=13$. Does this mean that the original polynomial can not be factorised further?