Gauss's Lemma: If an integer polynomial is reducible in $\mathbb Q[x]$, then it is reducible in $\mathbb Z[x]$.
It is obvious that if an integer polynomial is reducible in $\mathbb Z[x]$, then it is reducible in $\mathbb Q[x]$.
So: An integer polynomial is reducible in $\mathbb Q[x]$ if and only if it is reducible in $\mathbb Z[x]$.
A primitive polynomial is irreducible in $\mathbb Z[x]$ if and only if it is irreducible in $\mathbb Q[x]$
This may not hold if the polynomial is not primitive. Consider $2 \cdot x$, since $2$ is not a unit in $\Bbb{Z}[x]$, $2x$ is reducible in $\mathbb{Z}[x]$, but it is not reducible in $\Bbb{Q}[x]$.
Note that irreducible polynomials in $\Bbb{Z}[x]$ are always either constant or primitive, so you can also say that every irreducible polynomial in $\Bbb{Z}[x]$ is irreducible or a unit in $\Bbb{Q}[x]$.