II. A. Use synthetic division to find the quotient, Q(x) and the remainder R if P(x) is the dividend and D(x) is the divisor.

1. P(x) = 3x 4 - 5x ³ - 3x ² + 11x - 10 2. P(x) = x 4 + 2x ³ - 10x - 12 3. P(x) = 4x ³ + 5x ² - 23x + 6 4. P(x) = x 4 + 5x ³ + 7x ² - 8x + 9 5. P(x) = x + 3x ³ - 7x 4 + 2 6. P(x) = x 9 + 1 7. P(x) = 3x ³ - ix ² + 2x - 3i

D(x) = x - 5 D(x) = x + 3 D(x) = x - 2 D(x) = x + 5 D(x) = x - 1 D(x) = x - 1 D(x) = x - i

B. Determine whether the linear expressions given are factors of the given polynomial P(x).

8. P(x) = x ³ - 3x ² + 3x - 1

a) x - 1     b) x + 1     c) x - 2

9. P(x) = x ⁵ + 11x ³ - 12x

a) x - 1     b) x - 3     c) x + 5

ANSWERS

1. Q(x) = 3x ³ + 10x ² + 47x + 246; R = 1220

2. Q(x) = x ³ - x ² + 3x - 19; R = 45

3. Q(x) = 4x ² + 13x + 3; R = 12

4. Q(x) = x ³ + 7x - 43; R = 224

5. Q(x) = -7x ³ - 4x ² - 4x - 3; R = -1

6. Q(x) = x ⁸ + x ⁷ + x ⁶ + x ⁵ + x ⁴ + x ³ + x ² + x + 1; R = 2

7. Q(x) = 3x ² + 2ix; R = -3i

8. yes , no , no

9. yes, no, no