POLYNOMIALS REVIEW: PAST PROVINCIAL EXAM QUESTIONS
1. According to the Rational Root Theorem, determine all possible rational roots of: ?
A.
B.
C.
D.
2. If is a factor of , which of the following must have a value of 0?
A.
B.
C.
D.
3. How may real roots are there for the polynomial equation: ?
A. 1
B. 2
C. 3
D. 5
4. Factor
A.
B.
C.
D.
5. Determine the quotient when is divided by
A.
B.
C.
D.
6. If the cubic polynomial function passes through the point , determine the value of k
A.
B.
C.
D.
7. Determine the quotient when is divided by
A.
B.
C.
D.
8. Given the graph of below, which of the following best represents the graph of
A. B.
C. D.
9. Determine a real zero of the function graphed below:
A.
B.
C.
D.
10. Determine a factor of degree 2 of the polynomial if and
A.
B.
C.
D.
11. Determine the values of k for which is a zero of
A.
B.
C.
D.
12. If is a factor of the polynomial , which of the following must be true?
A.
B.
C.
D.
13. What is the maximum number of real roots that a polynomial equation can have if its degree is 6?
A. 3
B. 5
C. 6
D. 7
14. According to the Rational Zero Theorem, which number is a possible zero of the function ?
A.
B.
C.
D.
15. Which graph is the best representation of where
A. B.
C. D.
16. Determine the remainder when is divided by
A.
B. 18
C. 30
D. 52
17. Determine all the real zeros of the function
A.
B.
C.
D.
18. According to the Rational Root Theorem, which of the following is a possible root of the equation ?
A. 2
B. 3
C. 4
D. 8
19. When is divided by the remainder is 3. What is the value of k?
A.
B.
C.
D.
20. Which graph could represent a polynomial function of degree 5?
A. B.
C. D.
21. Solve
A.
B.
C.
D.
22. Determine the remainder when is divided by
A.
B.
C.
D.
23. Determine a polynomial equation with roots of , and 2
A.
B.
C.
D.
24. The graph of the cubic polynomial function is shown. Determine the equation of (i.e. move the graph down 4 units, then find the equation)
A.
B.
C.
D.
25. If the polynomial is divided by , which of the following represents the remainder?
A.
B.
C.
D.
26. Determine the value of k if 2 is a zero of the function
A.
B.
C.
D.
27. Determine the quotient when is divided by
A.
B.
C.
D.
28. If is a factor of the polynomial , where m and n are integers, according the Rational Root Theorem, which of the following could be a value for n?
A. 2
B. 6
C. 8
D. 10
29. Which graph is a possible representation of where a is a negative integer?
A. B.
C. D.
30. Determine a polynomial equation that has the following roots: 2,
A.
B.
C.
D.
31. When the polynomial is divided by the remainder is 6. Which of the following must be true?
A.
B.
C.
D.
32. Solve:
A.
B.
C.
D.
33. According to the Rational Root Theorem, which of the following equations has possible rational roots of
A.
B.
C.
D.
34. Which of the following is a polynomial function with zeros of , and ?
A.
B.
C.
D.
35. If , determine k if
A.
B.
C.
D.
36. The graph of the polynomial function , where a, b, c and d are constants, is shown below. What are the conditions on c and d?
A. ,
B. ,
C. ,
D. ,
37. Determine all real roots of the equation
A.
B.
C.
D.
38. Determine the minimum degree of the polynomial function graphed below.
A. 3
B. 4
C. 5
D. 6
39. The polynomial equation , where a, b, and c are integers, has 6 as one of its roots. According to the Rational Root Theorem, which of the following could be a value of c?
A. 2
B. 3
C. 9
D. 18
40. Determine the quotient and remainder:
A. quotient: , remainder:
B. quotient: , remainder:
C. quotient: , remainder:
D. quotient: , remainder:
41. Find the remainder when is divided by
A.
B.
C.
D.
42. Determine all real solutions for
A.
B.
C.
D.
43. If is a factor of , then the remaining two factors are
A. and
B. and
C. and
D. and
44. How many different real roots does the equation have?
A. 0
B. 1
C. 2
D. 3
45. Determine the polynomial function of degree 3 with zeros of , 0 and 3, that passes through the point . Answer may be left in factored form.
46. Determine the polynomial function of degree 3, with zeros 1, -3 and 2, and y-intercept -8. The answer may be left in factored form.
47. Graph the polynomial: . Label all the roots and the y-intercept.
48. Determine m so that is a factor of
49. Determine the polynomial function of degree 3 with zeros -1, 0 and 2, that passes through the point (1, -4). The answer may be left in factored form.
50. Graph the polynomial: Label all the roots and the y-intercept.
ANSWERS
1 / C / 12 / A / 23 / A / 34 / B2 / A / 13 / C / 24 / D / 35 / B
3 / C / 14 / C / 25 / A / 36 / A
4 / D / 15 / D / 26 / B / 37 / B
5 / B / 16 / D / 27 / B / 38 / D
6 / A / 17 / A / 28 / C / 39 / D
7 / D / 18 / B / 29 / B / 40 / A
8 / D / 19 / C / 30 / C / 41 / A
9 / A / 20 / B / 31 / A / 42 / C
10 / A / 21 / B / 32 / A / 43 / D
11 / C / 22 / D / 33 / D / 44 / C
45.
46.
47.
48. m - 19
49.
50.