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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.
This Theorem isn't repeating what you already know, but is instead trying to make your life simpler. When faced with a Factor Theorem exercise, you will apply synthetic division and then check for a zero remainder. 1  Use the Factor Theorem to determine whether x 1 is a factor of f (x) = 2x4 + 3x2 5x + 7.