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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.
Thenext example shows how the factor theorem can be used to solve a third-degreepolynomial equation. EXAMPLE 4 Solving a third-degree equationSuppose the equationx 3 4x 2 17x 60 0 is known to have a solution thatis an integer between 3 and 3 inclusive. Find the solution set.