The factor theorem. The Factor Theorem states that if f(a) = 0 for a polynomial then (x- a) is a factor of the polynomial f(x). Example. f(x) = x 2 + x - 6. f(x) = x 2 + x – 6 =. (x + 3)(x – 2) . f(-3) = (-3) 2 + (-3) – 6 =. 9 – 6 – 6 = 0. f(2) = 2 2 + 2 – 6 =. 4 + 2 – 6 = 0.

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