The rational root theorem states that for any polynomial equation
- an xn + an-1 xn -1 + ... + a1 x + a0 = 0
These root candidates can be tested using the Horner scheme. If a root is found, the Horner scheme will also yield a polynomial of degree n - 1 which is then to be investigated. After a polynomial is brought down to a quadratic equation, the quadratic formula may be used.
If the equation lacks a constant term a0, then 0 is one of the rational roots of the equation.
The theorem is a special case (for a single linear factor) of the Gauss lemma on factorization of polynomials.