6.1 Review Worksheet, Part 2 (continued)
+ − ÷ − x x
1 2
25. (2 x 2 + 3 x − 20) ÷ ( x − 2)
26.
27. (4 x 2 + 5 x + 1) ÷ ( x + 1)
2
x (2 13 8)
Use synthetic substitution to evaluate the polynomial for the given value. 28. P ( x ) = 2 x 2 − 5 x − 3 for x = 4
29. P ( x ) = 4 x 3 − 5 x 2 + 3 for x = − 1
1 3
4 5
30.
31.
2
3
2
P x x x x ( ) 3 5
x
2 for
= − x x ( ) 25 16 for P x
= − − +
=−
=
Determine whether the given binomial is a factor of the polynomial P ( x ). 32. ( x − 3); P ( x ) = 4 x 6 − 12 x 5 + 2 x 3 − 6 x 2 − 5 x + 10
33. ( x − 8); P ( x ) = x 5 − 8 x 4 + 8 x − 64
34. (3 x + 12); P ( x ) = 3 x 4 + 12 x 3 + 6 x + 24
35. An experimental electrical system has a voltage that can be modeled by V ( t ) = 0.5 t 3 + 4.5 t 2 + 4 t , where t represents time in seconds. The resistance in the system also varies and can be modeled by R ( t ) = t + 1. The current I is related to voltage and resistance by the equation = I V R . Write an expression that represents the current in the system.
50
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