Algebra 2 Companion Book, Volume 2

6.1.6 Synthetic Division and the Remainder and Factor Theorems - Worksheet

Example 1: Divide by using synthetic division. 1. (7 x 2 − 23 x + 6) ÷ ( x − 3)

2. ( x 4 − 5 x + 10) ÷ ( x + 3)

3. ( x 2 + x − 42) ÷ ( x + 7)

Example 2 and 3: Use synthetic substitution to evaluate the polynomial for the given value. 4. P ( x ) = 2 x 3 − 9 x 2 + 27 for x = 2 5. P ( x ) = x 2 − x − 30 for x = − 8

1 3

6.

7. P ( x ) = 3 x 5 + 4 x 2 + x + 6 for x = − 1

3

2

= + + + P x x x x x ( ) 3 5 4 2 for

=

Example 4 and 5: Determine whether the given binomial is a factor of the polynomial P ( x ). 8. ( x + 1); P ( x ) = 2 x 4 + 2 x 3 − x 2 − 5 x − 4

9. ( x − 2); P ( x ) = 5 x 3 + x 2 − 7

10. (2 x − 4); P ( x ) = 2 x 5 − 4 x 4 + 2 x 2 − 2 x − 4

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