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x â a is a factor of the polynomial f(x) if f(a) = 0. The Factor Theorem. If f(x) is a polynomial and f(p) = 0 then (x â p) is a factor of f(x). If f(x) is a polynomial and f(âq) = 0 then (x + q) is a factor of f(x). Polynomials-Factor Theorem. Description and examples of the Factor Theorem. Prove that (x + 1) is a factor of P(x) = x 2 + 2x + 1.
Definition of Rational Zeros Theorem. The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros).It provides a list of all possible rational roots of the polynomial equation, where all coefficients are integers.If the equation has rational roots p / q, where p and q are integers, then p must divide evenly into the constant term a 0 and q must divide evenly into the leading coefficient an.In other words, p is a factor of Â± a 0 and q is a factor of Â± an.efinition of Rational Zeros Theorem. The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros).