Name: Class: Date: A2 S2 Chpt 5 Review
Multiple Choice
Indicate the answer choice that best completes the statement or answers the question.
1. Solve b 4 + 2b 2 – 24 = 0.
a. –2, –
, c. –2, 2, –i
, 2
b. –
, i
, 2, 2i, i
d. –2i, 2i, –
, 2. If r is an odd integer and m = 8r, then will always be ____________.
a. odd
b. even
c. positive
3. Find the reciprocal of a. b. d. negative
.
c. d. x
4. Factor y3 – 64 completely.
a. (y – 4)3
b. (y – 4)(y + 4)2
c. (y – 4)(y2 + 4y + 16)
d. (y – 4)(y2 – 4y + 16)
5. One factor of x3 + 2x2 – 11x – 12 is x + 4. Find the remaining factors.
a. x + 1, x + 3
b. x – 1, x + 3
c. x + 1, x – 3
d. x – 1, x – 3
Choose the correct word or phase that best completes each sentence.
6. ____________ is a method for evaluating a polynomial function f(x) at a particular value of x.
a. End behavior
b. Synthetic substitution
7. A ____________ is a turning point where the graph increases as it approaches the point and decreases as it moves
away from the point.
a. relative maximum
b. depressed polynomial
8. The degree and ____________ of a polynomial function determines the graph’s end behavior.
a. relative minimum
b. leading coefficient
9. Writing the polynomial a. leading coefficients
as uses the idea of ____________.
b. quadratic form
10. The form we usually write in is called ____________.
a. standard notation
b. quadratic form
11. If is divided by x – 2, the quotient will be is called the ____________.
a. quadratic form
b. depressed polynomial
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and the remainder will be 0. In this case, Page 1
Name: Class: Date: A2 S2 Chpt 5 Review
12. A shelf in a lumber yard will safely hold up to 1000 pounds. A crate on the shelf is marked 270 pounds. What is the
greatest number of sheets of plywood, each weighing 7 pounds, that may safely be stacked on the shelf?
a. 103
b. 104
c. 105
d. 106
13. Which describes the number and type of roots of the equation x3 + 121x = 0?
a. 1 real root, 2 imaginary roots
b. 3 real roots
c. 2 real roots, 1 imaginary root
d. 3 imaginary roots
14. State the possible number of imaginary zeros of f (x) = 7x3 – x2 + 10x – 4.
a. exactly 1
b. exactly 3
c. 3 or 1
d. 2 or 0
15. What is the value of cd in the equation a. b. c. 2
?
d. –2
16. Use synthetic substitution to find f (3) for f (x) = x2 – 9x + 5.
a. –23
b. –16
c. –13
d. 41
17. Simplify (3x0y4)(2x2y)3.
a. 24x6y7
b. 216x6y5
c. 24x5
d. 6x6y7
18. One factor of x3 – 3x2 – 4x + 12 is x + 2. Find the remaining factors.
a. x + 2, x + 3
b. x + 2, x – 3
c. x – 2, x + 3
d. x – 2, x – 3
19. Which of the following is a rational zero of a. b. 1
20. Simplify a. c. .
d. 2
. Assume that no variable equals 0.
b. c. d. 21. Find p(–4) if p(x) = 3x3 – 2x2 + 6x – 4.
a. –252
b. –140
c. 132
d. 180
22. Which describes the number and type of roots of the equation x4 – 64 = 0?
a. 2 real roots, 2 imaginary roots
b. 3 real roots, 1 imaginary root
c. 4 real roots
d. 4 imaginary roots
23. Use synthetic substitution to find f (–2) for f (x) = 2x4 – 3x3 + x2 – x + 5.
a. 15
b. 67
c. 63
d. 19
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Page 2
Name: Class: Date: A2 S2 Chpt 5 Review
Use the graph.
24. Estimate the x-coordinate at which a relative minimum occurs.
a. 3
b. 2
c. 0
d. –1
Use the graph.
25. Determine the values of x between which a real zero is located.
a. between –2 and –1
b. between –1 and 0
c. between 0 and 1
d. between –3 and –2
26. Use synthetic substitution to find f (–3) for f (x) = x4 – 4x3 + 2x2 – 4x + 6.
a. 9
b. 225
c. 201
d. –15
27. Factor 27x3 – 1 completely.
a. (3x – 1)(9x2 + 3x + 1)
b. (3x – 1)3
c. (3x – 1)(9x2 – 3x – 1)
d. (3x – 1)(9x2 – 3x + 1)
28. If a. 15
, then what is the value of 5m6?
b. 30
c. 45
d. 135
29. Find all the rational zeros of p(x) = x3 – 12x – 16.
a. –2, 4
b. 2, –4
c. 4
d. –2
30. If mn = 16 and m2 + n 2 = 68, then (m + n)2 = ____________.
a. 68
b. 100
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c. 84
d. cannot be determined
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Name: Class: Date: A2 S2 Chpt 5 Review
31. Find p(–4) if a. 7
.
b. 71
c. 57
d. 39
32. Find p(–3) if p(x) = 4x3 – 5x2 + 7x – 10.
a. –94
b. 32
c. –184
d. –142
33. Simplify (5x – 4)2.
a. 25x2 – 16
b. 25x2 – 20x + 16
34. Solve x4 – 13x2 + 36 = 0.
a. –3, –2, 2, 3
b. –9, –4, 4, 9
35. Simplify a. c. 25x2 – 40x + 16
c. 2, 3, 2i, 3i
d. 25x2 – 18x – 16
d. –2, –3, 2i, 3i
.
b. c. d. Use the graph.
36. Estimate the x-coordinate at which a relative maximum occurs.
a. 1
b. –1
c. 2
d. –2
37. Maria is simplifying the expression (x3 – 6x)(2x3 + 5x – 1). Which of the following shows the correct product?
a. 2x6 – 7x4 – x3 – 30x2 + 6x
b. 2x9 – 7x4 – 11x3 – 30x2 + 6x
c. 2x9 – 8x3 – 30x2 + 6x
d. 2x6 + 5x4 – x3 – 11x2 – 6x
38. One factor of x3 + 4x2 – 11x – 30 is x + 2. Find the remaining factors.
a. x – 5, x + 3
b. x – 3, x + 5
c. x – 6, x + 5
d. x – 5, x + 6
39. Simplify a. Powered by Cognero
.
b. c. d. Page 4
Name: Class: Date: A2 S2 Chpt 5 Review
40. State the number of real zeros for the function whose graph is shown below.
a. 0
b. 2
41. Simplify a. c. 3
d. 1
. Assume that no variable equals 0.
c. 5y3z
b. d. Simplify.
42. a. b. c. d. Find all of the rational zeros of each function.
43. h(x) = x3 – 7x2 + 17x – 15
a. –3, 3
b. 3
c. 3i
d. no rational zeros
If p(x) = 3x 2 – 4 and r(x) = 2x 2 – 5x + 1, find each value.
44. r(a 2)
a. 8a 4 – 10a 2 + 1
b. 6a 8 – 4a 2 + 1
c. 2a 4 – 5a 2 + 1
d. –5a 2 + 1
45. r(x + 2)
a. x2 + x – 1
b. –2x2 – 3x + 1
c. 2x2 + 3x – 1
d. 4x
Use synthetic substitution to find f(–3) and f(4) for each function.
46. f(x) = x2 – 5x – 4
a. no solutions
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b. –10, –8
c. 20, 8
d. 20, –8
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Name: Class: Date: A2 S2 Chpt 5 Review
Find all zeros of each function.
47. q(x) = x4 + 50x2 + 49
a. 0
b. i, i, 7i, 7i
c. –i, i, –7i, 7i
d. –1, 1, –7, 7
48. g(x) = x4 + 4x3 – 3x2 – 14x – 8
a. 1, 1, 2, 4
b. –1, –1, 2, –4
c. –1i, –1, 2i, –4
d. 0
Find p(–2) and p(3) for each function.
49. p(x) = –x5 + 4x3
a. 0; 135
b. 20; –65
c. 0; –135
d. 34; 21
50. p(x) = –7x2 + 5x + 9
a. 29; 39
b. –29; –39
c. 27; –18
d. –19; –49
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
51. 3x3 – 4x2 – 17x + 6; x + 2
a. x + 2 is the only solution
b. x + 2, x + 2
c. x – 1, x – 1
d. x – 3, 3x – 1
Factor completely. If the polynomial is not factorable, write prime.
52. 6n 2 – 11n – 2
a. (6n – 1)(n – 2)
b. (6n + 1)(n – 2)
c. (6n + 2)
d. prime
53. x2 – 8x – 8
a. (x – 2)(x + 4)
b. (x – 8)(x + 1)
c. prime
d. x(x – 8)
54. BANKING Terry invests $1500 in two mutual funds. The first year, one fund grows 3.8% and the other grows 6%.
Write a polynomial to represent the amount Terry’s $1500 grows to in that year if x represents the amount he invested
in the fund with the lesser growth rate.
a. 0.022x + 1590
b. –0.022x + 1590
c. –0.022x – 1590
d. –1589.978x
List all of the possible rational zeros of each function.
55. s(x) = x4 – 8x3 + 7x – 14
a. 1, 2, 7, 14
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b. –1, –2, –7, –14
c. ±1, ±2, ±7, ±14
d. no rational zeros
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Name: Class: Date: A2 S2 Chpt 5 Review
56. g(x) = 5x3 + x2 – x + 8
a. –1, –2, –4, –8
b. ±1, ±2, ±4, ±8
c. 1, 2, 4, 8
d. no rational zeros
57. PHYSICS A proton in a magnetic field follows a path on a coordinate grid modeled by the function f(x) = x4 – 2x2 –
15. What are the x-coordinates of the points on the grid where the proton crosses the x-axis?
a. 5i, –5i
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b. c. d. Page 7