Let $f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_0$ be an irreducible polynomial over $\mathbb{Z}$.
Is there a way to construct a linear transformation $x = \alpha X + \beta$, where $\alpha, \beta \in \mathbb{Z}$ that yields the polynomial $g(X)$ that is reducible in $\mathbb{Z}$?
If a linear transformation is not possible, is there a simple rational function transformation of the form
$$x = {k(X) \over m(X)}$$
that yields $g(X)$ that is reducible in $\mathbb{Z}$?