Polynomials worksheet 3 levels

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Polynomials MCQ Worksheet

Easy Level

1. What is the degree of the polynomial "3x²+ 2x - 5"?

a) 1 b) 2 c) 3 d) 5

2. Which of the following is not a polynomial?

a) x³ - 2x² + x - 1 b) 3x + 2/x c) 2x² + 5 d) 4

3. Find the value of "x" in the polynomial equation: x² - 9 = 0.

a) -9 b) 3 c) ±3 d) ±9

4. What will be the sum of the coefficients of the polynomial (2x + 3)³?

a) 27 b) 8 c) 9 d) 6

5. If "x = 2" is a root of the polynomial "ax² + 5x + 6 = 0," what is the value of "a"?

a) 1 b) 2 c) 3 d) 4

6. The value of "k" for which the polynomial "x² + 3x + k" has equal roots is:

a) 3 b) 6 c) 9 d) -3

7. Which of the following polynomials has a degree of 1?

a) 4x³ + 2x² + 5x + 1 b) 2x² + 3x + 1 c) 5x⁴ + 3x² + 2 d) 6x² + 4x - 7

8. If "x = -3" is a root of the polynomial "2x² + kx + 12 = 0," find the value of "k."

a) -6 b) 6 c) 4 d) -4

9. The value of "p" for which the polynomial "x² + 5x + p" becomes a perfect square is:

a) 10 b) 25 c) 12.5 d) 15

10. If "x + 3" is a factor of the polynomial "ax² + bx + c," what can we say about the roots of the polynomial?

a) They are all real and distinct. b) They are all real but not necessarily distinct. c) They are all imaginary. d) They are all complex.

Medium Level

11. What is the value of "k" in the polynomial (2x - 3)(x + k) when divided by "x - 2" leaves a remainder of 5?

a) 7 b) 4 c) 3 d) 1

12. If "x = 1/2" is a root of the polynomial "2x³ - kx² + 2x - 3 = 0," find the value of "k."

a) 12 b) 8 c) 6 d) 4

13. Find the sum of all the coefficients in the polynomial (3x² + 4x + 1)⁴.

a) 7 b) 9 c) 17 d) 64

14. What is the remainder when the polynomial "4x³ - 3x² + 2x - 7" is divided by "2x - 1"?

a) 1 b) 3 c) 4 d) 7

15. If "x = -3" is a root of the polynomial "2x² + kx + 12 = 0," find the value of "k."

a) -6 b) 6 c) 4 d) -4

16. If "x = 3" is a root of the polynomial "x² + px - 9," find the value of "p."

a) 6 b) -6 c) 9 d) -9

17. What is the product of the roots of the polynomial "2x² - 5x + 3"?

a) 1 b) 2 c) 3/2 d) 3

18. If "x = -2" is a root of the polynomial "x³ + ax² + bx - 8," find the values of "a" and "b."

a) a = -5, b = -6 b) a = 5, b = 6 c) a = -4, b = -5 d) a = 4, b = 5

19. If "x = 1" is a root of the polynomial "2x³ - 3x² + kx - 6," find the value of "k."

a) -1 b) 0 c) 1 d) 2

20. The polynomial "P(x) = 2x³ + 3x² - kx + 7" is perfectly divisible by "x - 1." Find the value of "k."

a) 6 b) 4 c) 3 d) 2

Hard Level

21. If the polynomial "ax³ - 4x² + bx - 3" is perfectly divisible by "x + 1" and "x - 2," what are the values of "a" and "b"?

a) a = 2, b = 5 b) a = 3, b = -2 c) a = 1, b = -5 d) a = 4, b = 1

22. The polynomial "P(x) = x⁴ + ax³ + bx² + cx + 16" is divided by "x + 1" and leaves a remainder of 10. Find the value of "a + b + c."

a) -5 b) 5 c) 10 d) -10

23. If "x = 2" is a root of the polynomial "x³ + px² + qx + 1" and the sum of the other two roots is 3, find the value of "p" and "q."

a) p = 5, q = 4 b) p = 5, q = -4 c) p = -5, q = 4 d) p = -5, q = -4

24. The remainder when the polynomial "x³ - 2x² + 3x - 1" is divided by "x - 2" is:

a) 3 b) 6 c) 9 d) 11

25. If the polynomial "x³ + kx² + 9x - 10" is exactly divisible by "x - 2," find the value of "k."

a) 7 b) 8 c) 9 d) 10

26. The polynomial "ax³ + bx² + cx + 8" is divisible by "x + 2." If the polynomial also has "x - 1" as a factor, find the value of "a," "b," and "c."

a) a = 1, b = -2, c = 4 b) a = -1, b = 2, c = -4 c) a = 2, b = -4, c = 8 d) a = -2, b = 4, c = -8

27. The product of two zeros of the polynomial "x³ - 5x² + 6x + 8" is:

a) 2 b) 4 c) 8 d) -8

28. If the polynomial "x⁴ - kx³ + 9x² + 36x + 36" is divisible by "x + 3," find the value of "k."

a) 9 b) 18 c) 27 d) 36

29. If "x = 2" is a root of the polynomial "x³ + kx² - 16x + 32 = 0," find the value of "k."

a) -4 b) -2 c) 2 d) 4

30. If "x = -1" is a root of the polynomial "x³ + 3x² - kx + 2," find the value of "k."

a) 2 b) -2 c) 3 d) -3