 # 6-5: The Remainder and Factor Theorems Objective: Divide polynomials and relate the results to the remainder theorem.

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6-5: The Remainder and Factor Theorems Objective: Divide polynomials and relate the results to the remainder theorem.

Example 1

Remainder Theorem

Synthetic Division: A process for division of a polynomial by a binomial. Example 2: Divide

Step 1: Write the terms of the polynomial in descending order. Then write just the coefficients as shown.

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.

To write the result

Example 3:

Factor Theorem

Example 4 x = 2 Subtract 2 from both sides x – 2 = 0 So, x – 2 is a factor

The result gives the coefficients of the quotient.

HOMEWORK: AM Objectives #81 Divide Polynomials #82 Long division, factor higher term polynomials

Example 4 Factor

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

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