Prove that an integer monic polynomial with nonzero constant term and exactly one root outside the open unit disk is irreducible over $\mathbb{Q}$

Question

$\textbf{Problem:}$ Let $f(x)\in\mathbb{Z}[x]$ be a nonconstant monic polynomial, and let $\mathbb{D} = \{z ∈ C : |z| < 1\}$ be the open unit disk in the complex plane. Suppose that $f$ has exactly one root not in $\mathbb{D}$, and that its constant term $a_0$ is nonzero. Show that $f$ is irreducible over $\mathbb{Q}$.

$\textbf{Might be helpful:}$ Since only one root - let's call that root $\alpha_1$ - is not in $\mathbb{D}$, then $a_0<|\alpha_1|$. (the constant term of any polynomial is equal to the product of its roots over $\mathbb{C}$).

Answer 1

If $f=gh$ is a proper factorisation, one of its factors, $g$ say, has all zeroes in the unit disc. What could its constant term be?