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Remainder

Theorem!

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Division

  • Divide by
  • What is the remainder?
  • Evaluate

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Division

  • Divide

by

  • What is the remainder?
  • Evaluate

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What is Going On?

  • When
  • Then written as a division statement we have

where r is a constant (degree less than divisor)

  • Evaluate at x=a to get Remainder Theorem

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Why Use The Remainder Theorem?

  • Mostly to find factors
    • If r=0 then x-a is a factor of f(x)
  • Sometimes it leads to interesting algebraic problems
  • There are variations when the divisor is not x-a

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Examples

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Examples

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Examples

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