Are these polynomials irreducible in $\mathbb{Q}[x]$? $$x^3+x^2+x+1$$
$$x^5+x^3+x^2+1$$
$$x^5+x^3+x+1$$
I've tried applying Eisenstein criterion but I can't figure it out.
Thanks in advance.

$$x^3+x^2+x+1=(x+1)(x^2+1)$$
$$x^5+x^3+x^2+1=(x^2+1)(x^3+1)$$
For $f(x)=x^5+x^3+x+1$, we have $f(2)=43$, which is prime, so by Cohn's criterion, $f(x)$ is irreducible over $\mathbb{Z}$.
