6-5:%20The%20Remainder%20and%20Factor%20Theorems

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6-5The Remainder and FactorTheorems
Objective Divide polynomials and relate the
results to the remainder theorem.
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Example 1
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Remainder Theorem
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Synthetic Division A process for division of a
polynomial by a binomial.
Example 2 Divide
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Step 1 Write the terms of the polynomial in
descending order.
Then write just the coefficients as shown.
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Step 2 Write the constant k, of the divisor x
k to the left
Bring the first coefficient down. Multiply the
first coefficient by k and write the product
under the second coefficient. Add the second
column. Write the sum as shown.
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To write the result
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Example 3
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Factor Theorem
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Example 4
x 2
Subtract 2 from both sides
x 2 0
So, x 2 is a factor
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The result gives the coefficients of the
quotient.
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• HOMEWORK
• AM Objectives
• 81 Divide Polynomials
• 82 Long division, factor higher term
  polynomials

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Example 4 Factor
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Use synthetic division to find the other factors.
The result gives the coefficients quotient