Rational root theorem
= Rational root theorem
{wiki}
If a primitive polynomial
$$
a_nX^n+\cdots+a_0\in\mathbb Z[X]
$$
has a rational root $r/s$ in lowest terms, then $r\mid a_0$ and $s\mid a_n$. In particular, a monic integer polynomial can have only integer rational roots dividing its constant term.