Solution
= Solution
The <Eisenstein criterion> says that a primitive <polynomial>
$$
f(X)=a_nX^n+\cdots+a_0\in\mathbb Z[X]
$$
is irreducible if there is a prime $p$ such that
$$
p\nmid a_n,
\qquad
p\mid a_i\quad(0\leq i<n),
\qquad
p^2\nmid a_0.
$$
By the <Gauss lemma for polynomials>, irreducibility over $\mathbb Q$ and over $\mathbb Z$ agree for primitive <polynomials>.