Synthetic Division

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Synthetic Division
Lesson Created by Carol Keller

• Pre-Calculus
• Objective 3.A
• Students will use synthetic division to test
  for zeros of a function.

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First, lets review polynomial division.
So, 3x3- x2- 3x 1 divided by x 1.. equals 3x2
4x 1
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Now , lets convert to Synthetic Division

• We use only the coefficients of each term
• We change x 1 into 1..the actual test zero of
  the function
• Instead of Multiply , Subtract, Multiply,
  Subtract
• ..WE now Multiply, ADD, Multiply, ADD..

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3x3- x2- 3x 1 divided by x 1..
becomes.
Remainder is 0
Translates into 3x2- 4x 1
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Lets compare the two side by side
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We still need to remember to insert Zeros for
terms that are omitted.
For example, 4x5 3x3 1translates into .
4 0 -3 0 0 1