Main Page | See live article | Alphabetical index The rational root theorem states that for any polynomial equation an xn + an-1 xn -1 + ... + a1 x + a0 = 0 with integer coefficients (and an nonzero), every rational solution x (also called "root") is of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an. 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.