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.