Eisenstein criterion on almost cyclotomic polynomial

Question

Let's consider the equation:

$f(X) = x^5 + x^4 + x^3 + x^2 + x + 1$

How does one proof with the Eisenstein criterion (it has to be with this one) that this polynomial is irreducible in $\mathbb{Z}[X]$? I already tried to prove it for $f(X+1)$, since I thought this is the $5^{th}$ cyclotomic polynomial, but this is the $6^{th}$, and $6$ is no prime number, so it doesn't work.

Thank you in advance.

Answer 1

The polynomial isn't irreducible, since $f(-1) = 0$. So I guess, it was a typo, and it was indeed meant to be the $5^{th}$ cyclotomic polynomial.