The Math Meridian
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The factor theorem: factor cubics

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Useful for: IB Math AA HL AP® Precalculus

Learn it (x − a) is a factor of P(x) exactly when P(a) = 0. Test the factors of the constant term to find one root, divide (or compare coefficients) to get a quadratic, then factor that.

Example: Factor x³ − 2x² − 5x + 6.

  1. Try x = 1: 1 − 2 − 5 + 6 = 0, so (x − 1) is a factor.
  2. Divide: x² − x − 6 = (x − 3)(x + 2).
  3. (x − 1)(x − 3)(x + 2).

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