Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior
to match the function with its graph.
1)
f(x) =8x3+ 2x2– 4x + 2
1)
A)
falls to the left and falls to the right
B)
rises to the left and rises to the right
C)
rises to the left and falls to the right
D)
falls to the left and rises to the right
2)
f(x) =3x4–5x2
2)
A)
falls to the left and rises to the right
B)
falls to the left and falls to the right
C)
rises to the left and falls to the right
D)
rises to the left and rises to the right
Determine the x–intercepts of the graph of the quadratic function. Then match the function with its graph.
3)
y =x2– 4x –12
3)
A)
B)
C)
D)
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior
to match the function with its graph.
4)
f(x) = – 8x3+ 2x2+ 4x – 1
4)
A)
rises to the left and rises to the right
B)
falls to the left and falls to the right
C)
falls to the left and rises to the right
D)
rises to the left and falls to the right
4
5)
f(x) = – 4x2– 3x – 1
5)
A)
falls to the left and falls to the right
B)
rises to the left and falls to the right
C)
rises to the left and rises to the right
D)
falls to the left and rises to the right
6)
f(x) =2x2+ 2x – 3
6)
A)
falls to the left and rises to the right
B)
falls to the left and falls to the right
C)
rises to the left and rises to the right
D)
rises to the left and falls to the right
6
Determine the x–intercepts of the graph of the quadratic function. Then match the function with its graph.
7)
y =x2– 6x +8
7)
A)
B)
C)
D)
Factor completely, or state that the polynomial is prime.
8)
9x2+ 42x + 49 – 4y2
8)
A)
(3x +7+2y)(3x +7–2y)
B)
(3x –7+2y)(3x –7–2y)
C)
prime
D)
(3x +7+2y)(3x –7–2y)
A
7
C
9)
147x2+ 378xy + 243y2
9)
A)
3(7x + 9y)2
B)
3(7x + 9y)(7x – 9y)
C)
3(7x – 9y)2
D)
prime
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
10)
(7x – y)2
10)
A)
49x2+y2
B)
49x2–7xy +y2
C)
49x2–14xy +y2
D)
49x2–14xy – 2y2
C
Add the polynomials. Assume all variable exponents represent whole numbers.
11)
(–9x2y – xy) + (6x2y +7xy)
11)
A)
15x2y +6xy
B)
15x2y +8xy
C)
–3x2y +6xy
D)
–3x2y +8xy
C
Use factoring to solve the quadratic equation.
12)
15x2+ 37x + 20 = 0
12)
A)
5
3, 4
5
B)
–1
3, –1
5
C)
5
3, –4
5
D)
–5
3, –4
5
D
13)
x2
28 –11
28 x + 1 = 0
13)
A)
{–1, 0}
B)
{3, 8}
C)
{4, 7}
D)
1
4, 1
7
C
A
Use the Leading Coefficient Test to describe the end behavior of the graph of the polynomial function.
14)
f(x) = – 11x2+110x
14)
A)
rises to the left and rises to the right
B)
falls to the left and rises to the right
C)
rises to the left and falls to the right
D)
falls to the left and falls to the right
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
15)
24x9y9z2– 36x5y4z3– 60x7y2z4
15)
A)
x5y2z2(24x4y7– 36y2z – 60x2z2)
B)
12(2x9y9z2– 3x5y4z3– 5x7y2z4)
C)
12x5y2z2(2x4y7– 3y2z – 5x2z2)
D)
12x5y2z3(2x4y7– 3y2– 5x2z)
Solve the problem.
16)
An architect is allowed 24 square yards of floor space to add a small room to a house. Because of
the room’s design in relationship to the existing structure, the width of the rectangular floor must
be –2 yards less than two times the length. Find the length and the width of the rectangular floor
that the architect is permitted.
16)
A)
length: 8 yd, width: 3 yd
B)
length: 4 yd, width: 3 yd
C)
length: 3 yd, width: 4 yd
D)
length: 3 yd, width: 8 yd
Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
17)
11ab2(5a2b3+2ab)
17)
A)
55a3b4+22a2b3
B)
55a2b5+22a2b3
C)
55a3b5+22a2b3
D)
55a3b5+22a2b2
9
Subtract the polynomials. Assume all variable exponents represent whole numbers.
18)
(5x8+ 3x6– 11x2+ 5) – (2x8– 11x4+ 6x2– 12)
18)
A)
–3x8+ 3x6– 11x4– 17x2+ 17
B)
–3x8+ 3x6+ 11x4– 17x2+ 17
C)
3x8+ 3x6+ 11x4– 17x2+ 17
D)
3x8+ 3x6– 11x4– 17x2+ 17
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
19)
(9an– 8bn)(9an+ 8bn)
19)
A)
81an– 64bn
B)
9a2n – 8b2n
C)
81a2n – 64b2n
D)
81a2n + 144anbn– 64b2n
C
Give the requested components for the polynomial.
20)
x8–12x6; the degree of each term and the coefficient of each term
20)
A)
degrees: 1 and –12; coefficients: 8 and 6
B)
degrees: 1 and 8; coefficients: –12 and 6
C)
degrees: 8 and 6; coefficients: 0 and 12
D)
degrees: 8 and 6; coefficients: 1 and –12
D
Determine whether the graph shown is the graph of a polynomial function.
21)
21)
A)
Yes
B)
No
B
C
Factor using the formula for the sum or difference of two cubes.
22)
216x6+27y6
22)
A)
(6x2–3y2)(36x4+18x2y2+9y4)
B)
(6x –3y)(36x2+18xy +9y2)
C)
(6x2+3y2)(36x4–18x2y2+9y4)
D)
(6x +3y)(36x2–18xy +9y2)
Use factoring to solve the quadratic equation.
23)
x2+ 4x – 96 = 0
23)
A)
{–12, 8}
B)
{–12, 1}
C)
{12, –8}
D)
{12, 8}
A
Factor completely, or state that the polynomial is prime.
24)
36y2+93y +60
24)
A)
prime
B)
3(20y +4)(y +5)
C)
3(3y + 1)(4y +20)
D)
3(3y +4)(4y +5)
D
Factor by grouping. Assume any variable exponents represent whole numbers.
25)
x2+2x +5x +10
25)
A)
(x +2)(x2+5)
B)
(x2+2)(x +5)
C)
(x –2)(x –5)
D)
(x +2)(x +5)
D
Factor by grouping to obtain the difference of two squares.
26)
x2– 14x + 49 –y2
26)
A)
(x – 7 + y)(x – 7 – y)
B)
(x – 7 – y)2
C)
(x – 7 + y)(x + 7 – y)
D)
(x + 7 + y)(x + 7 – y)
A
11
C
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
27)
(x + y +10)2
27)
A)
x2+y2+20x +20y +100
B)
x2+y2+100
C)
x2+ 2xy +y2+20x +20y +100
D)
x2+ 2xy +y2+100
Factor completely, or state that the polynomial is prime.
28)
x8– 1
28)
A)
prime
B)
(x2– 1)4
C)
(x4+ 1)(x2+ 1)(x + 1)(x – 1)
D)
(x4– 1)2
29)
x3y –49xy3
29)
A)
prime
B)
xy(x +7y)2
C)
xy(x +7y)(x –7y)
D)
xy(x –7y)2
Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
30)
–7x5(–7x – 8)
30)
A)
49x6– 8
B)
49x6+ 56x5
C)
105x5
D)
49x + 56
Factor using the formula for the sum or difference of two cubes.
31)
64x3– 1
31)
A)
(4x – 1)(16x2+ 1)
B)
(64x – 1)(x2+ 4x + 1)
C)
(4x – 1)(16x2+ 4x + 1)
D)
(4x + 1)(16x2– 4x + 1)
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
32)
(x –9)(x2–2)
32)
A)
x3–11x +18
B)
x3–11x2+18
C)
x3+9x2+2x +18
D)
x3–9x2–2x +18
Factor using the formula for the sum or difference of two cubes.
33)
343y3– 1000
33)
A)
(7y – 10)(49y2+ 70y + 100)
B)
(7y + 10)(49y2– 70y + 100)
C)
(7y – 10)(49y2+ 100)
D)
(343y – 10)(y2+ 70y + 100)
Multiply the monomials. Assume any variable exponents represent whole numbers.
34)
(10x6y5z)(–2x4yz3)
34)
A)
8x10y6z4
B)
8x24y5z3
C)
–20x24y5z3
D)
–20x10y6z4
Factor the trinomial, or state that the trinomial is prime.
35)
x2– 8x + 12
35)
A)
(x + 2)(x – 6)
B)
prime
C)
(x – 2)(x – 6)
D)
(x + 2)(x + 1)
Factor using the formula for the sum or difference of two cubes.
36)
a3b3+64
36)
A)
(ab +4)(a2b2–16)
B)
(ab –4)(a2b2+4ab +16)
C)
(ab +4)(a2b2–4ab +16)
D)
(ab –4)(a2b2+16)
13
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
37)
(an+ 16bn)2
37)
A)
an+ 32anbn+ 256bn
B)
a2n + 16anbn+ 256b2n
C)
an + 2 + 32anbn+ 256bn + 2
D)
a2n + 32anbn+ 256b2n
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
38)
(11 –y5)(11 +y5)
38)
A)
121 –y5
B)
121 –y10
C)
121 –y25
D)
y10 –121
Use factoring to solve the quadratic equation.
39)
17x2=7x
39)
A)
7
17 , 0
B)
–17
7, 0
C)
17
7, 0
D)
–7
17 , 0
Factor by grouping. Assume any variable exponents represent whole numbers.
40)
x2+5x –2x –10
40)
A)
(x +5)(x +2)
B)
(x –5)(x –2)
C)
(x –5)(x +2)
D)
(x +5)(x –2)
Use factoring to solve the quadratic equation.
41)
2–10x = (3x – 7)(x + 1)
41)
A)
{–1, 3}
B)
–1, 7
3
C)
1
5
D)
{–3, 1}
14
Solve the problem.
42)
A flagpole is supported by a wire fastened 39 feet from its base. The wire is 13 feet longer than the
height it reaches on the flagpole. Find the length of the wire.
42)
A)
52 ft
B)
65 ft
C)
71 ft
D)
48 ft
43)
The public swimming pool, which is a rectangle measuring 31 meters by 32 meters, needs a new
deck. The deck of uniform width that will surround the pool will be made of concrete. There is only
enough money in the budget to cover 3040 square meters with concrete. How wide should the path
be?
43)
A)
14 m
B)
20 m
C)
16 m
D)
18 m
Factor completely, or state that the polynomial is prime.
44)
10x2–20
44)
A)
prime
B)
10(x –2)2
C)
10(x2–2)
D)
10(x +2)(x –2)
Subtract the polynomials. Assume all variable exponents represent whole numbers.
45)
(7x4+5xy –y3) – (x4+9xy +5y3)
45)
A)
6x4– 4xy – 4y3
B)
7x4– 4xy – 6y3
C)
8x4+ 17xy + 4y3
D)
6x4– 4xy – 6y3
46)
(9x6+ 17x4– 13) – (3x6– 6x4– 12)
46)
A)
28x10
B)
6x6+ 23x4– 25
C)
6x6+ 23x4– 1
D)
6x6+ 20x4– 25
15
Factor by grouping. Assume any variable exponents represent whole numbers.
47)
x3+ 9x – 2x2– 18
47)
A)
(x – 2)(x + 9)
B)
(x + 2)(x2+ 9)
C)
(x – 2)(x2– 9)
D)
(x – 2)(x2+ 9)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
48)
x4–1
48)
A)
(x2+1)(x +1)(x –1)
B)
(x2+1)2
C)
prime
D)
(x2–1)2
Factor completely, or state that the polynomial is prime.
49)
7x5–7x
49)
A)
7x(x2+ 1)(x + 1)(x – 1)
B)
7x(x4+ 1)(x2+ 1)(x + 1)(x – 1)
C)
prime
D)
7x(x2+ 1)(x2– 1)
50)
500x3+5xy2
50)
A)
5x(10x + y)(10x – y)
B)
5x(10x2+y2)
C)
x(500x2+5y2)
D)
prime
Add the polynomials. Assume all variable exponents represent whole numbers.
51)
(7x8+ 9x7– 4x6+ 8) +(7x8– 4x7+ 9x6+ 4)
51)
A)
4x8+ 4x7+ 11x6+ 16
B)
24x42 + 12
C)
14x8+ 5x7+ 5x6+ 12
D)
14x16 + 5x14 + 5x12 + 12
16
Solve the problem.
52)
The net income y (in millions of dollars) of Pet Products Unlimited from 2010 to 2012 is given by
the equation y = 9x2+ 15x + 52, where x represents the number of years after 2010. Assume this
trend continues and predict the year in which Pet Products Unlimited’s net income will be $1306
million.
52)
A)
2020
B)
2022
C)
2023
D)
2021
Perform the indicated operations.
53)
(3x3y – 5x2y – 9y) +(7x3y – 3x2y + 5y + 3)
53)
A)
10x3y + 8x2y – 4y + 3
B)
10x3y – 8x2y + 4y + 3
C)
10x3y – 8x2y – 4y + 3
D)
10x3y – 8x2y – 4y – 3
Factor completely, or state that the polynomial is prime.
54)
x2y –36y +144 –4x2
54)
A)
(y +4)(x +6)(x –6)
B)
(y –4)(x +6)(x –6)
C)
prime
D)
(y –4)(x2+36)
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
55)
(11x2–3y)2
55)
A)
22x4–33x2y +6y2
B)
121x4–66x2y +9y2
C)
121x2–66x2y +9y2
D)
121x4–130x2y +9y2
56)
(x – 13)2
56)
A)
x2– 26x + 169
B)
x + 169
C)
169x2– 26x + 169
D)
x2+ 169
Give the requested components for the polynomial.
57)
–7x9+5x8+2x; the degree of the polynomial and the leading coefficient of the polynomial.
57)
A)
degrees: 9, 8, and 1; coefficients: –7, 5, and 2
B)
degree: 9; coefficient: –7
C)
degree: –7; coefficient: 9
D)
degrees: –7, 5, and 2; coefficients: 9, 8, and 0
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
58)
–42x2n –18xn
58)
A)
–6xn(7xn+3)
B)
–6xn(7xn–3x)
C)
–6xn(7xn–3)
D)
–6x2n(7xn+3)
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
59)
54x9y9– 12x2y7+ 30x5y2
59)
A)
x2y2(54x7y7– 12y5+ 30x3)
B)
6x2(9x7y9– 2y7+ 5x3y2)
C)
6x2y2(9x7y7– 2y5+ 5x3)
D)
6(9x9y9– 2x2y7+ 5x5y2)
Evaluate.
60)
If f(x) =3x3+4x2– x +9, find f(0) and f(–2).
60)
A)
f(0) =9; f(–2) =3
B)
f(0) =9; f(–2) = – 1
C)
f(0) =9; f(–2) =51
D)
f(0) =16; f(–2) =3
18
Evaluate the polynomial function.
61)
If f(x) =x2+ 8x + 9, find f(a – 3).
61)
A)
a2+ 8a + 3
B)
a2+ 8a – 6
C)
a2+ 2a + 15
D)
a2+ 2a – 6
Factor completely, or state that the polynomial is prime.
62)
18x2+ 24x + 8
62)
A)
2(3x – 2)2
B)
2(3x + 2)2
C)
2(3x + 2)(3x – 2)
D)
prime
B
Perform the indicated operations.
63)
(9y – 5)2
63)
A)
81y2– 90y – 25
B)
81y2– 90y + 25
C)
81y2+ 25
D)
81y2– 25
B
Find the product. Assume all variable exponents represent whole numbers.
64)
(4x2+ 5x + 4)(x2– 2x + 1)
64)
A)
4x4– 8x3– 2x2– 3x + 4
B)
4x4– 8x3– 6x2– 3x + 4
C)
4x4– 3x3– 2x2– 3x + 4
D)
4x4– 3x3– 6x2– 3x + 4
C
Factor completely, or state that the trinomial is prime.
65)
12x4+ 52x3–224x2
65)
A)
4x2(3x –8)(x +7)
B)
4x2(3x +8)(x –7)
C)
4x2(3x –8)(x –7)
D)
prime
A
19
D
66)
18x3– 50x2+28x
66)
A)
2x(9x +7)(x +2)
B)
prime
C)
x(9x – 7)(2x – 2)
D)
2x(9x – 7)(x – 2)
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
67)
x2–49
67)
A)
(x +7)2
B)
prime
C)
(x –7)2
D)
(x +7)(x –7)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
68)
2x3y –72xy
68)
A)
prime
B)
xy(x +6)(2x –12)
C)
2y(x +6)(x2–6x)
D)
2xy(x +6)(x –6)
Factor the trinomial by grouping, or state that the trinomial is prime.
69)
5y2–27y +28
69)
A)
(5y –7)(5y +4)
B)
(5y –7)(y –4)
C)
(5y +4)(y –7)
D)
5(y –7)(y –4)
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
70)
–3x2–6x +27
70)
A)
–3(x2+2x –9)
B)
–3x(x2+2x –9)
C)
3(x2–2x +9)
D)
–3(x2–2x +9)
20