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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 Factor Theorem. The factor theorem is a theorem linking factors and zeros of a polynomial. It is commonly applied to factorizing and finding the roots of polynomial equations. The theorem states that isa factor of a polynomial f (x)if ;that is, r is a root of f (x). Factor theorem problems are typically solved by applying synthetic division and then checking for a zero remainder.