I am looking for criteria for the irreducibility of monic polynomials with constant term $\pm1$ over $\mathbb Q$. Eisenstein's criterion clearly doesn't apply here.

For instance, for the family of polynomials $$ p_n(x)=x^n-x^{n-1}-1 $$ Wolfram Alpha suggests that $p_n$ is probably irreducible for $n\ge6$. How does one show this?