Unit 3: Lesson 6: The Remainder and Factor Theorems Practice
1. How many possible positive zeros does the function below have?
f(x) = 3×3 - 2×2 + 4x + 1
A. 0
B. 0 or 2
C. 1 or 3
D. 0, 1, 2, or 3
2. How many possible negative zeros does the function below have?
f(x) = 4×3 – 6×2 + 8x – 5
A. 0
B. 0 or 2
C. 1 or 3
D. 0, 1, 2, or 3
3. How many real roots does the following equation have?
x4 - 81 = 0
A. 4
B. 2
C.1
D. 0
4. How many imaginary roots are there in the equation below?
x3 + 9x = 0
A. 0
B. 1
C. 2
D. 3
5. The polynomial x3 – 4×2 – 29x – 24 has a factor of x – 8. Find the remaining factors.
A. (x – 3)(x – 1)
B. (x + 3)(x + 1)
C. (x – 1)(x + 67)
D. (x – 67)(x + 1)
6. The polynomial 3×3 + 10×2 - x - 12 has a factor of x + 3. Find the remaining factors.
A. (3x + 4)(x - 1)
B. (3x - 1)(x + 4)
C. (3x - 4)(x + 1)
D. (3x + 1)(x - 4)
7. If g(x) = 3×4 + x3 – 2×2 + x + 12, find g(-4).
A. 680
B. 816
C. 744
D. 880
8. If f(x) = -3×5 – x + 2×3 – 1, what is f(2)?
A. 15
B. 99
C. -25
D. -83
9.Solve.
A. 0
B. 2
C. -2
D. not enough information to tell
10. Solve.
A. 13
B. -4
C. 4
D. -13
