 Rational root theorem

If a primitive polynomialhas 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.

The Rational Root Theorem is a useful tool in algebra for finding the possible rational roots of a polynomial equation. It states that if a polynomial \( P(x) \) with integer coefficients has a rational root \( \frac{p}{q} \) (in lowest terms), where \( p \) and \( q \) are integers, then: - \( p \) (the numerator) must be a divisor of the constant term of the polynomial.