Dividing Polynomials

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Section 5.4

• Dividing Polynomials

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Review of Long Division

• What terms do we use to describe 672 and 21?
• Because the reminder is zero, we know that 21 is
  a factor of 672.
• How could you write 672 using the divisor and
  quotient?

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• Writing the ratio of

• Writing P(x) in terms of the divisor, quotient,
  and remainder

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Using long division to Divide polynomials
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Is a factor of
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Synthetic Division

• Synthetic division simplifies the long division
  by using only the zero of the divisor and the
  coefficients of the dividend
• Example 3

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The polynomial
expresses the volume, in cubic inches, of a
shadow box. What are the dimensions of the box
if one side is x 5?
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Remainder Theorem

• If you divide a polynomial P(x) of degree ngt1 by
  x a, then the remainder is P(a)
• Example
• What is the remainder when
• Is divided by x 3?
• How many ways could you find the remainder?
• Which is most efficient?