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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.
For example, 60 = 22.31.51. We can reword the Fundamental Theorem this way: the canonical factorization of an integer greater than one is unique. This theorem (and indeed any theorem labeled fundamental) should not be taken too lightly. There are many number systems in which factorizations are not unique.