The Math Meridian
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The remainder theorem

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Useful for: IB Math AA HL AP® Precalculus

Learn it When P(x) is divided by (x − a), the remainder is P(a). So you can find a remainder without long division: just substitute x = a.

Example: Remainder when x³ − 4x + 5 is divided by x + 2?

  1. Divide by x − (−2), so substitute x = −2.
  2. (−8) − 4(−2) + 5 = 5.

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