5.4 Dividing Polys

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5.4 Dividing Polys
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Example 1Divide x23x-12 byx-3
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• We say x23x-12 divided by x-3 is x6 with
  remainder of 6, or x6, R6.
• We can use division to check if we have factors
  to a given poly.
• Example 2 Determine if x4 is a factor of
  x26x8, the remainder will be zero if it is a
  factor.
• You try

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Synthetic Division

• A simplified process, we no long have to use long
  division to divide polys.
• Example 3 We will use synthetic division to
  divide 3x3-4x22x-1 by x1

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• You Try
• Use Synthetic Division to divide
• x34x2x-6 by x1.
• Answer x23x-2 R -4

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The Remainder Theorem

• If a poly P(x) of degree n1 is divided by
  (x-a), where a is a constant, then the remainder
  is P(a).
• Example Use synthetic division for
• P(x)x4-5x24x12 to find P(-4).
• We get R as 172 so P(-4)172,
• P(-4) (-4)4-5(-4)24(-4)12 172

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• HW pg 308 9, 21, 22, 23, 25, 32, 34