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Published byDamian Wilkerson Modified over 5 years ago

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6-5: The Remainder and Factor Theorems 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

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