Remainder and Factor Theorems

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Remainder and Factor Theorems
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The Remainder Theorem

• If a polynomial f(x) is divided by x-a, the
  remainder is the constant f(a), and
• Dividendquotient divisor remainder
• Where is a polynomial with degree one
  less than the degree of f(x)

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The Remainder Theorem
Remember Lesson 5-3 for Synthetic Division
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The Remainder Theorem
Remainder 1
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The Factor Theorem
Since the remainder is 0, x-3 is a factor of the
polynomial.
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The Factor Theorem

• When you divide the polynomial by one of the
  binomial factors , the quotient is called a
  depressed equation.

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The Factor Theorem
Remainder 10, therefore
(x-2) Is NOT a factor
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The Factor Theorem

• Given a polynomial and one of its factors, find
  the remaining factors of the polynomial. Some
  factors may not be binomials.