Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the correct factored form of the given equation.
1)
2x2+ 2x – 24
1)
A)
2(x + 3)(x – 4)
B)
(x + 3)(x – 4)
C)
2(x – 3)(x – 4)
D)
2(x – 3)(x + 4)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
2)
What steps would you take to factor x2+ 5x + 6?
2)
3)
If an object is dropped, the distance it falls after t seconds is given by d =1
2gt2. A student is
determining how long it would take an object to fall 84 feet on planet x having gravity 10
ft/sec2. The student determines the two solutions t = ± 84
5. Are both correct answers? Why
or why not?
3)
4)
A student is solving the equation x2=8x This student has decided to divide both sides of
the equation by x and finds the solution x =8. The student checks the answer in the back of
the book and finds that x = 0 is also a solution. The student feels that this is a misprint.
How would you advise him or her?
4)
5)
A student is told that there are two solutions to the problem 2x2=2x. The student can
only find one; that is, x = 1. How could you advise this student?
5)
6)
A student is trying to solve the equation (x + 3)(x – 9) =8. The student has set x + 3 =8 and
x – 9 =8 and found that two solutions x =5, x =17. The student checks his or her results by
plugging in his or her solutions into the original equation and finds that they do not work.
How would you advise him or her?
6)
1
7)
In factoring a trinomial in y as (y+ a)(y+ b), what must be true of a and b, if the coefficient
of the last term of the trinomial is positive?
7)
8)
Suppose you have to solve the following problem: “The length of a rectangle is 5 ft more
than its width and its area is 84 square feet. Find its width and length.” Let x represent the
width of the rectangle and translate the problem into an equation. Do not solve the
equation.
8)
Explanation:
Answer the question.
9)
The binomial 49x2+ 196 is the sum of two squares that can be factored. Why is this
possible?
9)
Explanation:
Provide an appropriate response.
10)
Tom’s teacher asks him to solve the following problem: “The product of two consecutive
even numbers is 168. Find the numbers.” Tom rewords the problem and translates to the
following equation:
x(x + 1) = 168
Why is this equation not correct and what would the correct equation be?
10)
Explanation:
Answer the question.
11)
Why is the answer (x2– 81)(x2+ 81) not the correct answer to the instruction “Factor (x4
– 6561) completely”?
11)
Explanation:
Provide an appropriate response.
12)
Explain the error in the following:
x2+ 2x – 15 = (x – 5)(x + 3)
12)
x2+ 2x – 15 = (x + 5)(x – 3)
Explanation:
Explanation:
13)
Mark’s teacher asked him to solve the following problem: “One leg of a right triangle is 7
m longer than the other. The length of the hypotenuse is 13 m. Find the lengths of the legs.”
Mark translated the problem into the following equation: (x2+ 7) +x2=132. Why is this
equation not correct and what would the correct equation be?
13)
14)
Give an example of three numbers whose greatest common factor is 10.
14)
15)
Why is 11 called a triple solution to the equation (x – 11)3= 0?
15)
16)
A student was trying to solve the problem 9x(2x – 7) = 0. The student knew that he or she
should set 2x – 7 = 0 but was confused about whether or not he or she should set 9x = 0, or
9= 0 and x = 0. How would you advise this student?
16)
17)
How could you solve the equation (6x + 9)(8x – 5)(9x – 2) = 0? How many equations do
you need to solve? What are their solutions?
17)
18)
The height of an object after t seconds is given by the equation h = –16t2+ 9t + 9. When
h = 0, solving for t means finding the time when the object hits the ground. A student uses
the quadratic formula and finds 2 solutions. One is negative and the other positive. Which
solution makes sense? Which does not? Why?
18)
19)
Use the FOIL method to show that (5x + 10)(x – 3) is 5x2– 5x – 30. If you were asked to
completely factor 5x2– 5x – 30, why would it be incorrect to give (5x + 10)(x – 3) as your
answer?
19)
3
20)
Brenda’s teacher asks her to solve the following problem: “The product of two consecutive
numbers is 210. Find the numbers.” Brenda knows that she must translate this problem into
an equation. What equation could Brenda write to represent this problem?
20)
21)
Tina was asked to solve the following problem: “The product of two consecutive numbers is
90. Find the numbers.” Tina’s solution is given below. Do you agree with her conclusion? If
not, why not?
x(x + 1) = 90
x2+ x = 90
x2+ x – 90 = 0
(x + 10)(x – 9) = 0
x = –10 or x = 9
The pair of numbers is 9 and 10
21)
22)
What steps would you take to factor x2– 2x – 15?
22)
23)
Jason is given the following information: “The shortest side of a triangle is 4 cm less than
the middle side. The length of the longest side is 13 cm.” Jason claims that he can find the
lengths of the two shorter sides by solving the following equation:
x2+(x + 4)2=132
What is wrong with his reasoning?
23)
24)
A student is told that there are two solutions to the problem 3x2=3x. The student can
only find one, namely, x =1. How can you advise him or her?
24)
25)
Maria’s teacher asked her to solve the following problem: “One leg of a right triangle is 5 m
longer than the other. The length of the hypotenuse is 25 m. Find the lengths of the legs.”
Maria called the legs x and y and translated the problem into the following equation:
x2+y2=252. After that she was unsure of how to proceed. Why is Maria’s equation not
very useful? Write the correct equation and find the solution to the problem showing all
the steps of your work.
25)
26)
Write a problem in which the quadratic equation x(x + 3) = 108 must be solved in order to
solve the problem.
26)
27)
A student is solving the equation s2=62 and has determined that s =6. He or she has
looked up the answer in the back of the book and finds that s = –6 is also a solution. The
student feels that this is a misprint. How would you advise him or her?
27)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor completely.
28)
(m + n)b2+ (m + n)b +15(m + n)
28)
A)
b(m + n)(b +16)
B)
(m + n)(b2– b +15)
C)
(m + n)(b +15)(b –15)
D)
(m + n)(b2+ b +15)
5
Complete the factoring.
29)
x2+ 12x + 27 = (x + 3)( )
29)
A)
x + 24
B)
x2+ 9
C)
x + 9
D)
x – 15
Factor completely.
30)
x2– 1.8x + 0.81
30)
A)
(x – 0.9)2
B)
(x + 0.9)(x – 0.9)
C)
(x + 0.9)2
D)
Prime
Solve the problem.
31)
Two cars leave an intersection. One car travels north; the other east. When the car traveling north
had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the
car heading east. How far had the eastbound car traveled?
31)
A)
30 mi
B)
20 mi
C)
15 mi
D)
25 mi
Factor completely. If the polynomial is prime, say so.
32)
3x2+ x –4
32)
A)
(3x +4)(x – 1)
B)
(3x +4)(x –3)
C)
(3x + 1)(x – 1)
D)
(3x –4)(x + 1)
Factor completely.
33)
(x + y)3–(x – y)3
33)
A)
2y(3x2–y2)
B)
y(3x2+y2)
C)
y(3x2–y2)
D)
2y(3x2+y2)
6
Factor completely. If the polynomial cannot be factored, write prime.
34)
u2– 7u +12
34)
A)
(u + 3)(u + 4)
B)
(u – 3)(u – 4)
C)
(u – 3)(u + 4)
D)
(u + 3)(u – 4)
Provide an appropriate response.
35)
Is it possible to factor the expression 7x2(y + 2) + 7(y + 2)? If so, factor it.
35)
A)
No
B)
Yes: 7x2(y + 9)
C)
Yes: (y + 2)(7x2+ 7)
D)
Yes: 7x2(y + 2) + 7
Solve the equation.
36)
x2+7x +6= 0
36)
A)
{–6}
B)
{6, –1}
C)
{–6, –1}
D)
{–6, 1}
Provide an appropriate response.
37)
Is x5y8 a common factor of x6y10 and x4y8?
37)
A)
No
B)
Yes
Factor out the greatest common factor.
38)
12x8y9+ 18x6y7+ 30x4y4
38)
A)
6x4y4(2x4y5+ 3x2y3+ 5)
B)
No common factor (except 1)
C)
6(2x8y9+ 3x6y7+ 5x4y4)
D)
6x4(2x4y9+ 3x2y7+ 5y4)
7
Factor by grouping.
39)
18r2+63ry –2xr –7xy
39)
A)
(2r +7y)(9r – x)
B)
(7r +2y)(9r – x)
C)
(2r +7y)(x –9r)
D)
(2r +7y)(9x – r)
Factor completely. If the polynomial is prime, say so.
40)
x2– x – 6
40)
A)
(x + 3)(x – 2)
B)
(x + 2)(x – 3)
C)
(x + 1)(x – 6)
D)
Prime
41)
y2=25y
41)
A)
{25}
B)
{0, 5}
C)
{–5, 5}
D)
{0, 25}
42)
49k2– 36m2
42)
A)
(7k + 6m)(7k – 6m)
B)
(7k + 6m)2
C)
(7k – 6m)2
D)
Prime
43)
x2– x =20
43)
A)
{–4, 5}
B)
{–4, –5}
C)
{4, 5}
D)
{1, 20}
Factor by grouping.
44)
t2+5t +7t +35
44)
A)
t(t + 47)
B)
(t +5)(t+7)
C)
(t +5)(t–7)
D)
(t –5)(t–7)
Solve the problem.
45)
The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.
45)
A)
15, 16
B)
0, 1 or 16, 17
C)
0, 1
D)
0, 1 or 15, 16
46)
49t3– 9t = 0
46)
A)
{0}
B)
3
7
C)
–3
7, 3
7, 0
D)
3
7, –3
7
47)
5w –5x +5w2–5x2
47)
A)
5(w – x)(1 + w – x)
B)
(w – x)(1 + w + x)
C)
5(w – x)(1 + w + x)
D)
5(w – x)(w + x)
Factor out the greatest common factor.
48)
120x8y9+ 120x3y7+ 84x6y2
48)
A)
12x3(10x5y9+ 10y7+ 7x3y2)
B)
No common factor (except 1)
C)
12(10x8y9+ 10x3y7+ 7x6y2)
D)
12x3y2(10x5y7+ 10y5+ 7x3)
9
Factor completely.
49)
b2–38b +361
49)
A)
(b +19)(b –19)
B)
(b +19)2
C)
(b –19)2
D)
Prime
Solve the equation.
50)
16s3– 44s2+ 11s = –19s
50)
A)
3
2, 5
4, 0
B)
3
2, 5
4
C)
3
2, –3
2
D)
{0}
Simplify.
51)
83
51)
A)
24
B)
4
C)
512
D)
11
Solve the problem.
52)
A parallelogram has a base of length x + 7 and a height of x + 2 and has an area of 50 square units.
Find the base and height of the parallelogram. (A = bh)
52)
A)
height = 1 unit; base = 50 units
B)
height = 5 units; base = 10 units
C)
height = 6.25 units; base = 8 units
D)
height = 2 units; base = 25 units
Factor completely.
53)
p5q2–3p4q3–18p3q4
53)
A)
p3q2(p + q)(p –3q)
B)
p3q2(p –6q)(p +3q)
C)
p3q2(p –6q)(p + q)
D)
p3q2(p +6q)(p –3q)
Solve the equation.
54)
36k2– 49 = 0
54)
A)
6
7, 0
B)
7
6, –7
6
C)
6
7, –7
6
D)
{7, 0}
55)
5x2–45x = 5x( )
55)
A)
x –9
B)
9–x2
C)
9– x
D)
x2–9
Solve the problem.
56)
The diagram below shows a rope connecting the top of a pole to the ground. The rope is 21 yd long
and touches the ground 18 yd from the pole. How tall is the pole? Round approximations to the
nearest tenth.
?21 yd
18 yd
56)
A)
5.4 yd
B)
19.5 yd
C)
58.5 yd
D)
10.8 yd
Solve the equation.
57)
30x2=10 +44x
57)
A)
1
5, 5
3
B)
–1
5, 1
C)
1
5, –5
3
D)
–1
5, 5
3
11
58)
(x – 5)2+x2=(x + 5)2
58)
A)
{–20}
B)
{0, 20}
C)
{0, –20}
D)
{20}
Factor completely. If the polynomial is prime, say so.
59)
49x2– 81
59)
A)
(7x + 9)(7x – 9)
B)
Prime
C)
(7x – 9)2
D)
(7x + 9)2
Solve the problem.
60)
The area of a square is numerically 3 less than the perimeter. Find the length of the side, if the side
is greater than 1.
60)
A)
12 units
B)
6 units
C)
3 units
D)
5 units
Factor completely. If the polynomial is prime, say so.
61)
x4–81
61)
A)
(x +3)2(x –3)2
B)
(x2+9)(x +3)(x –3)
C)
Prime
D)
(x2–9)(x +3)(x –3)
62)
64a9b2, 40a6b9
62)
A)
4a3b7
B)
8a9b9
C)
320a9b9
D)
8a6b2
Factor by grouping.
63)
27 –3y –9p +yp
63)
A)
(9 –y)(3+p)
B)
(9 +y)(3–p)
C)
(9 +y)(3+p)
D)
(9 –y)(3–p)
Solve the problem.
64)
The table shows the population of a city for five years.
Year Population (in millions of people)
2007 65
2008 65.5
2009 67
2010 69
2011 71.5
This data was used to develop the quadratic equation y = 0.373x2+ 0.165x + 65, which models the
population of the city y in millions in the year x, where x = 0 represents 2007, x = 1 represents 2008,
and so on. Use the model to find the estimated population in the year 2009.
64)
A)
1,490,000,000,000
B)
66,822,000
C)
1,490,000
D)
65,538,000
Factor completely.
65)
4y4–18y3+18y2
65)
A)
2y2(2y +3)(y –3)
B)
y2(2y –3)(y –3)
C)
2y2(2y –3)(y +3)
D)
2y2(2y –3)(y –3)
Factor completely. If the polynomial is prime, say so.
66)
30y2–25y
66)
A)
5y(6y +5)
B)
y(30y –25)
C)
5y(6y –5)
D)
–5y(6y +5)
67)
16x2–24xy +9y2
67)
A)
Prime
B)
(4x – y)2
C)
(3x +4y)2
D)
(3x –4y)2
Factor the polynomial completely.
68)
x3– 125
68)
A)
(x + 125)(x2– 1)
B)
(x + 5)(x2– 5x + 25)
C)
(x – 5)(x2+ 5x + 25)
D)
(x – 5)(x2+ 25)
Complete the factoring.
69)
7x2y6+21x2y5= 7x2y5( )
69)
A)
7y +3x
B)
x2y +3
C)
y +3x2
D)
y +3
Solve the equation.
70)
x2+ 3x – 40 = 0
70)
A)
{–8, 1}
B)
{–8, 5}
C)
{8, 5}
D)
{8, –5}
Factor completely.
71)
22x4y2+58x3y2–24x2y2
71)
A)
x2y2(x –3)(11x +4)
B)
2x2y2(x +3)(11x –4)
C)
2(x +3)(11x –4)
D)
2x2y2(x +3)(11x +4)
14
72)
3x2– 12x + 12
72)
A)
Prime
B)
(3x – 6)(x – 2)
C)
3(x – 2)(x – 2)
D)
3(x – 4)(x + 1)
Solve the equation.
73)
15p4+ 16p2 =32p3
73)
A)
4
5, 4
3, 0
B)
4
3, 4
5
C)
32
5, –32
5
D)
{0}
A
Factor the polynomial completely.
74)
343y3– 512
74)
A)
(7y – 8)(49y2+ 56y + 64)
B)
(343y – 8)(y2+ 56y + 64)
C)
(7y + 8)(49y2– 56y + 64)
D)
(7y – 8)(49y2+ 64)
A
Factor out the greatest common factor.
75)
3m(6– m) + 2n(6– m)
75)
A)
(3m + 2n)(6– m)
B)
(3m – 2n)(6– m)
C)
No common factor (except 1)
D)
m(3+ 2n)(6– 1)
A
15
C
76)
64m2–9
4
76)
A)
8m –3
22
B)
8m +3
28m –3
2
C)
8m +3
22
D)
Prime
Solve the equation.
77)
x2+16x +64 = 0
77)
A)
{8, 1}
B)
{8}
C)
{–8}
D)
{–8, 0}
Solve the problem.
78)
A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30
meters longer than the length of the longer leg. How long is the longer leg?
78)
A)
150 m
B)
180 m
C)
90 m
D)
120 m
Solve the equation.
79)
(x – 3)(x2+ 15x + 56) = 0
79)
A)
{–3, 7, 8}
B)
{3, –7, –8}
C)
{3}
D)
{–3}
16
Solve the problem.
80)
The table shows the population of a city over the past five years.
Year Population (in millions of people)
1995 65
1996 65.5
1997 67
1998 69
1999 71.5
We used these data to develop the quadratic equation y = .373x2+ .165x + 65, which models the
population of the city y in millions in the year x, where x = 0 represents 1995, x = 1 represents 1996,
and so on. Use the model to find the estimated population in the year 1998.
80)
A)
68,852,000
B)
71,628,000
C)
1,490,000,000,000
D)
1,490,000
Factor completely.
81)
9r2(y +2)5–12r(y +2)5–5(y +2)5
81)
A)
(y +2)5(9r –5)(r +1)
B)
(y +2)5(3r –5)(3r +1)
C)
(y +2)5(3r +5)(3r –1)
D)
(y +2)5(3r –5)(3r –1)
Factor out the greatest common factor.
82)
2x(3x – 2) – 5(3x – 2)
82)
A)
(6x – 5)(x – 2)
B)
(6x + 5)(x + 2)
C)
(2x – 5)(3x – 2)
D)
(2x + 5)(3x + 2)
Factor completely.
83)
4y2+ 18y – 10
83)
A)
Prime
B)
2(2y – 1)(y + 5)
C)
(4y – 2)(y + 5)
D)
2(2y + 1)(y – 5)
17
84)
512p3– 1
84)
A)
(8p – 1)(64p2+ 8p + 1)
B)
(512p – 1)(p2+ 8p + 1)
C)
(8p – 1)(64p2+ 1)
D)
(8p + 1)(64p2– 8p + 1)
85)
Find a quadratic equation having the given solutions.
x = – 5
7 or x = – 6
7
85)
A)
7x2+ 11x + 30= 0
B)
49x2+ 77x + 30 = 0
C)
7x2– 11x – 30= 0
D)
49x2– 77x + 30 = 0
86)
9x2– 39x – 30
86)
A)
Prime
B)
(9x + 6)(x – 5)
C)
3(3x + 2)(x – 5)
D)
3(3x – 2)(x + 5)
87)
15m2– 22mn + 8n2= (3m – 2n)( )
87)
A)
5m – 4n
B)
5m – 4n2
C)
5m + 4n
D)
m + 4n
Factor completely. If the polynomial is prime, say so.
88)
–4x2+40x –100
88)
A)
4(x +5)2
B)
4(x –5)2
C)
–4(x –5)2
D)
Prime
18
Factor completely.
89)
84x2+ 49xy + 7y2
89)
A)
7(3x – y)(4x – y)
B)
Prime
C)
(21x + 7y)(4x + y)
D)
7(3x + y)(4x + y)
Factor by grouping.
90)
6x2– 15xy + 10xy – 25y2
90)
A)
(3x + 5)(2x – 5)
B)
(6x + 5y)(x – 5y)
C)
(3x + 5y)(2x – 5y)
D)
(3x – 5y)(2x – 5y)
C
Solve the equation.
91)
n2–196= 0
91)
A)
{–14, 14}
B)
{0, 14}
C)
{14}
D)
{–14}
A
Provide an appropriate response.
92)
Is it possible to factor the expression 8x2(y + 5) + 7(y – 5)? If so, factor it.
92)
A)
Yes: (8x2+ 7 + 5 + y)
B)
Yes: (8x2+ 7)(y – 5)
C)
No
D)
Yes: (8x2+ 7)(y + 5)
C
Solve the problem.
93)
Suppose a pyramid has a rectangular base whose width is 4 centimeters less than its length. If the
height is 5 centimeters and the volume is 35 cubic centimeters, find the length of the base.
V =1
3Bh
93)
A)
4 cm
B)
21 cm
C)
3 cm
D)
7 cm
D
D
Factor the polynomial completely.
94)
375k3m – 24m4
94)
A)
(15km – 6m2)(25k2+ 4m2)
B)
3m(5k + 2m2)(25k2– 10km + 4km2)
C)
3m(125k – 2m)(k2+ 10km + 4m2)
D)
3m(5k – 2m)(25k2+ 10km + 4m2)
95)
x4y8, xy7
95)
A)
x4y7
B)
y7
C)
x4y8
D)
xy7
D
96)
Is x3y6z4 a common factor of x4y7z5and –x3y7z4?
96)
A)
Yes
B)
No
A
Solve the equation.
97)
(3y + 25)(7y + 18) = 0
97)
A)
–3
22, –7
18
B)
–25
3, –18
7
C)
25
3, 18
7
D)
{22, 11}
B
98)
r(r –12) = –36
98)
A)
{–6}
B)
{36, 6}
C)
{6}
D)
{6, –6}
C
D
Factor by grouping.
99)
5p3+6q3+6pq2+5p2q
99)
A)
(p +q2)(6p2+5q)
B)
(p2+q2)(5p +6q)
C)
(p2+q2)(6p +5q)
D)
(p2+q2)(6p –5q)
Factor completely.
100)
12y5–6y4+9y2
100)
A)
3y2(4y3+2y2–3)
B)
3y2(4y3–2y2+3)
C)
3y(4y4–2y3+3y)
D)
3y2(4y3–2y2+3y)
Solve the equation.
101)
x(x –6) =40
101)
A)
{4, 10}
B)
{–4, 10}
C)
{4, –10}
D)
{–4, –10}
102)
If an object is propelled upward from ground level with an initial velocity of 80.1 feet per second,
its height h in feet t seconds later is given by the equation h = –16t2+80.1t. After how many
seconds does the object hit the ground?
102)
A)
0.2 sec
B)
5.0 sec
C)
2.5 sec
D)
10.0 sec
Factor completely.
103)
4x2– 20x + 25
103)
A)
(2x – 5)(2x + 5)
B)
(2x + 5)2
C)
(2x – 5)2
D)
Prime
21
104)
9p2(r +6)6+48pq(r +6)6+64q2(r +6)6
104)
A)
(r +6)6(3p + q)2
B)
(r +6)6(3p +8q)2
C)
(r +6)6(3p –8q)2
D)
(r +6)6(3p +8q)(3p –8q)
Factor completely. If the polynomial is prime, say so.
105)
x2+36
105)
A)
(x +6)(x –6)
B)
(x –6)2
C)
Prime
D)
(x +6)2
Factor completely.
106)
t2+2
5t +1
25
106)
A)
t –1
52
B)
t +1
52
C)
t +1
5t –1
5
D)
Prime
Factor out the greatest common factor.
107)
24y – 72
107)
A)
72
B)
No common factor (except 1)
C)
24(y – 3)
D)
24y
Factor by grouping.
108)
20x2– 15x + 8x – 6
108)
A)
(5x + 2)(4x – 3)
B)
(5x – 2)(4x + 3)
C)
(20x – 2)(x + 3)
D)
(20x + 2)(x – 3)
22
109)
9s2– 16t4
109)
A)
(3s – 4t2)2
B)
(3s + 4t2)2
C)
(3s + 4t2)(3s – 4t2)
D)
Prime
110)
104x3, 52x9
110)
A)
104x3
B)
26x6
C)
52x3
D)
78x3
Solve the problem.
111)
A rectangle has a length of x + 3 and a width of x – 3, and has an area of 40 square units. Find the
length and width of the rectangle. (A = LW)
111)
A)
width = 2 units; length = 20 units
B)
width = 4 units; length = 10 units
C)
width = 5 units; length = 8 units
D)
width = 1 unit; length = 40 units
Factor by grouping.
112)
9y2+ 18y + 8
112)
A)
(3y + 4)(3y + 2)
B)
(9y + 4)(y + 2)
C)
(3y – 4)(3y – 2)
D)
Prime
Factor the binomial completely. If it is prime, say so.
113)
4x2+ 25
113)
A)
(2x + 5)(2x – 5)
B)
(2x + 5)2
C)
(2x – 5)2
D)
Prime
23
Factor the binomial completely. If it is prime, say so.
Factor out the greatest common factor.
114)
3x2y7+15x2y6
114)
A)
x2y6(3y +5)
B)
3x2y6(y +5)
C)
y +5
D)
3x6y2(y +5)
Factor completely. If the polynomial cannot be factored, write prime.
115)
x2– x – 42
115)
A)
(x + 1)(x – 42)
B)
(x + 7)(x – 6)
C)
(x + 6)(x – 7)
D)
Prime
116)
The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in
this roof plan. Round approximations to the nearest tenth.
6 ft
11 ft
116)
A)
8.5 ft
B)
6.3 ft
C)
12.5 ft
D)
78.5 ft
Factor completely.
117)
x2– 6xy + 9y2
117)
A)
(x – 3y)2
B)
(x – 3y)(x + 3y)
C)
(x + 3y)2
D)
Prime
Find the greatest common factor of the terms.
118)
18r, 27
118)
A)
18
B)
9r
C)
9
D)
54r
Factor completely. If the polynomial is prime, say so.
119)
4wx –2wy –2xz + yz
119)
A)
(2wz)(2x – y)
B)
(2 – z)(2wx – y)
C)
(2w + z)(2x + y)
D)
(2w – z)(2x – y)
Factor by grouping.
120)
6m3–2m2n2–3mn +n3
120)
A)
(2m2– n)(3m –n2)
B)
(2m2– n)(3m +n2)
C)
(2m – n)(3m2–n2)
D)
(2m2+ n)(3m –n2)
121)
15z2+ 14z – 8
121)
A)
(3z – 4)(5z + 2)
B)
(15z + 4)(z – 2)
C)
(3z + 4)(5z – 2)
D)
Prime
Solve the equation.
122)
b(b + 19) = 0
122)
A)
{–19, 0}
B)
{–1, –19}
C)
{1, –19}
D)
{19, 0}
Complete the factoring.
123)
x2+ 2x – 35 = (x – 5)( )
123)
A)
x – 7
B)
x2+ 5
C)
5– x
D)
x + 7
25
Factor out the greatest common factor.
124)
t(4– m) + s(4– m)
124)
A)
t(4– m) + s
B)
(t + s)(4– m)
C)
(t – s)(4– m)
D)
No common factor (except 1)
Factor by grouping.
125)
20x2+ 27x + 9
125)
A)
(20x + 3)(x + 3)
B)
(4x – 3)(5x – 3)
C)
(4x + 3)(5x + 3)
D)
Prime
Solve the problem.
126)
The product of two consecutive integers is 89 more than their sum. Find the integers.
126)
A)
10, 11
B)
–9, –8
C)
10, 11 or –9, –8
D)
9, 10 or –9, –8
Solve the equation.
127)
(x – 7)2+x2=(x + 1)2
127)
A)
{7, –1}
B)
{7, 12}
C)
{–4, –12}
D)
{4, 12}
Factor the polynomial completely.
128)
z6+ 1
128)
A)
(z3+ 1)(z3– 1)
B)
(z + 1)(z– 1)(z2+z+ 1)(z2–z+ 1)
C)
(z2+ 1)(z4–z2+ 1)
D)
(z + 1)(z– 1)(z4–z2+ 1)
26
129)
8, 10, 20
129)
A)
4
B)
2
C)
8
D)
1
130)
–28z8= –7z6( )
130)
A)
–4z2
B)
196z
C)
4z6
D)
4z2
Solve the equation.
131)
(x – 2)(x + 4) = 0
131)
A)
{2, –2, 4, –4}
B)
{2, 4}
C)
{2, –4}
D)
{–2, 4}
Solve the problem.
132)
A parallelogram has a base of length 2x + 1 and a height of x + 3 and has an area of 42 square units.
Find the base and height of the parallelogram. (A = bh)
132)
A)
height = 14 units; base = 3 units
B)
height = 3 units; base = 14 units
C)
height = 6 units; base = 7 units
D)
height = 7 units; base = 6 units
Factor the binomial completely. If it is prime, say so.
133)
9x2– 16
133)
A)
(3x + 4)(3x – 4)
B)
(3x + 4)2
C)
(3x – 4)2
D)
Prime
Factor completely. If the polynomial is prime, say so.
134)
2x2– 16x + 32
134)
A)
(2x – 8)(x – 4)
B)
Prime
C)
2(x – 4)(x – 4)
D)
2(x – 16)(x + 1)
Solve the equation.
135)
4x(x + 5) = (3x – 9)(x + 5)
135)
A)
{5, 9}
B)
{–9}
C)
{–5, –9}
D)
{9}
C
Factor by grouping.
136)
9x2+ 12xt + 4t2
136)
A)
(9x + 2t)(x + 2t)
B)
(3x – 2t)(3x – 2t)
C)
(3x + 2t)(3x + 2t)
D)
Prime
C
Find the greatest common factor of the terms.
137)
21m4, 189m9
137)
A)
21m5
B)
189m4
C)
3969m5
D)
21m4
D
Factor completely. If the polynomial is prime, say so.
138)
y3–27
138)
A)
(y +3)(y2–3y –9)
B)
(y –3)(y2+3y +9)
C)
(y –3)(y2+3y –9)
D)
(y –3)(y2–9)
B
C
Factor completely.
139)
–2r2+15rt –7t2
139)
A)
(2r – t)(r –7t)
B)
–1(2r – t)(r –7t)
C)
–1(2r + t)(r –7t)
D)
–1(2r + t)(r +7t)
Factor out the greatest common factor.
140)
48m9– 120m6– 48m3
140)
A)
24m3 (2m6– 5m3– 2)
B)
24(2m9– 5m6– 2m3)
C)
m3(48m6– 120m3– 48)
D)
No common factor (except 1)
D)
Factor completely.
141)
4x3+ 8x2y – 32xy2=4x( )( )
141)
A)
x – 2y, x + 4y
B)
x + 2y, x – 4y
C)
x + 8xy, x – 4y
D)
x + 8y, x – 4y
D)
Solve the equation.
142)
(3x)2=(3x + 6)2–(x + 6)2
142)
A)
{24}
B)
{0, 24}
C)
{–24, 0}
D)
{–24}
D)
Factor completely. If the polynomial is prime, say so.
143)
10y4– 35y3– 20y2
143)
A)
5y2(2y – 1)(y + 4)
B)
Prime
C)
5y2(2y + 1)(y – 4)
D)
y2(10y – 5)(y + 4)
D)
D)
Answer the question.
144)
The monomial 64x16y4 is a perfect square.
True or False?
144)
A)
False.
B)
True.
145)
3k3–24
145)
A)
3(x –2)(x2+4)
B)
3(x +2)(x2–2x +4)
C)
(3x –2)(x2+2+12)
D)
3(x –2)(x2+2x +4)
146)
The area of a square is numerically 165 more than the perimeter. Find the length of the side.
146)
A)
15 units
B)
113 units
C)
450 units
D)
60 units
147)
A rectangular garden has dimensions of 25 feet by 11 feet. A gravel path of equal width is to be
built around the garden. How wide can the path be if there is enough gravel for 352 square feet?
147)
A)
6 ft
B)
6.5 ft
C)
4 ft
D)
5 ft
Factor completely.
148)
x2+13xy +42y2
148)
A)
x(x +13y +42y2)
B)
(x +6y)(x –7y)
C)
(x +6y)(x +7y)
D)
(x –6y)(x –7y)
30
Solve the equation.
149)
x2+ 4x – 45 = 0
149)
A)
{9, –5}
B)
{9, 5}
C)
{–9, 1}
D)
{–9, 5}
Solve the problem.
150)
The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and
added to the width, the figure becomes a square with an area of 100 square inches. What are the
dimensions of the original figure?
150)
A)
8 in. by 10 in.
B)
10 in. by 10 in.
C)
8 in. by 12 in.
D)
6 in. by 10 in.
Factor completely.
151)
x2+ 12x + 36
151)
A)
(x – 6)2
B)
(x + 6)(x – 6)
C)
(x + 6)2
D)
Prime
Factor completely. If the polynomial cannot be factored, write prime.
152)
x2– 6x – 55
152)
A)
(x – 5)(x + 1)
B)
(x + 5)(x – 11)
C)
(x – 5)(x + 11)
D)
Prime
Solve the problem.
153)
The product of two consecutive integers is 55 more than their sum. Find the integers.
153)
A)
–7, –6
B)
7, 8 or –7, –6
C)
8, 9 or –7, –6
D)
8, 9
154)
A rectangle has a length of x + 5 and a width of x – 5 and has an area of 56 square units. Find the
length and width of the rectangle. (A = LW)
154)
A)
width = 1 unit; length = 56 units
B)
width = 2 units; length = 28 units
C)
width = 7 units; length = 8 units
D)
width = 4 units; length = 14 units
Factor completely. If the polynomial cannot be factored, write prime.
155)
s2+5s +6
155)
A)
(s +6)(s – 1)
B)
(s +6)(s +5)
C)
(s +3)(s +2)
D)
(s –3)(s –2)
C
Solve the problem.
156)
A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30
meters longer than the length of the longer leg. How long is the longer leg?
156)
A)
150 m
B)
90 m
C)
180 m
D)
120 m
D
157)
Find three consecutive integers such that the square of the sum of the smaller two is 240 more than
the square of the largest.
157)
A)
7, 9, 11
B)
9, 10, 11
C)
–9, –8, –7
D)
9, 10, 11, or –9, –8, –7
D
Factor completely.
158)
216x2– 360x +150
158)
A)
6(36x2– 60x +25)
B)
(36x – 30)(6x – 5)
C)
6(6x + 5)(6x – 5)
D)
6(6x – 5)2
D
32
D
Answer the question.
159)
The monomial 16x2y8 is a perfect square.
True or False?
159)
A)
True.
B)
False.
160)
What values of n will make xn a perfect square?
160)
A)
n must be a power of 3.
B)
n must be a multiple of 5.
C)
n must be odd.
D)
n must be even.
161)
Product: –16 Sum: –6
161)
A)
–8 and 2
B)
8 and –2
C)
16 and –1
D)
–16 and 1
162)
12r2=3r
162)
A)
0, 1
4
B)
1
4
C)
{0}
D)
{0, 4}
163)
3r2– 26r – 9 = 0
163)
A)
1
26, –1
3
B)
–1
3, 3
C)
–1
3, 9
D)
{–3, 9}
Factor completely.
164)
–x2–7x +18
164)
A)
–1(x –9)(x +2)
B)
–1(x +9)(x –2)
C)
–1(x –9)(x –2)
D)
(x +9)(x –2)
Find the pair of numbers whose product and sum are given.
165)
Product: 112 Sum: 22
165)
A)
14 and 8
B)
–14 and 8
C)
–14 and –8
D)
14 and –8
Factor by grouping.
166)
9x2+ 9xt + 2t2
166)
A)
(9x + t)(x + 2t)
B)
(3x – t)(3x – 2t)
C)
(3x + t)(3x + 2t)
D)
Prime
Solve the problem.
167)
The height of a box is 7 inches. The length is three inches more than the width. Find the width if the
volume is 910 cubic inches.
167)
A)
130 in.
B)
10 in.
C)
13 in.
D)
7 in.
168)
x(x –30) = –225
168)
A)
{15}
B)
{–15}
C)
{30}
D)
{15, –15}
Complete the factoring.
169)
42x9=7x( )
169)
A)
6x
B)
6x8
C)
294x8
D)
294x10
Factor by grouping.
170)
15x2+ 20x – 9x – 12
170)
A)
(15x – 3)(x + 4)
B)
(5x – 3)(3x + 4)
C)
(5x + 3)(3x – 4)
D)
(15x + 3)(x – 4)
B
Solve the equation.
171)
x(6x + 30) = 0
171)
A)
{0, –5}
B)
0, –1
5
C)
0, 1
5
D)
{0, 5}
A
Factor completely.
172)
8x2y2+ 2xy2– 15y2
172)
A)
(4x + 3y)(2x – 5y)
B)
y2(2x + 3)(4x – 5)
C)
y2(x + 3)(8x – 5)
D)
(2x + 3y)(4x – 5y)
B
Factor the binomial completely. If it is prime, say so.
173)
32a4b – 98b3
173)
A)
2b(4a2+ 7b)(4a2– 7b)
B)
2b(4a + 7b)2
C)
2b(4a – 7b)2
D)
Prime
A
B
Factor completely.
174)
(5m + n)p2–11(5m + n)p +30(5m + n)
174)
A)
(5m + n)(p +5)(p +6)
B)
(5m + n)(p –5)(p +6)
C)
(5m + n)(p2–11p +30)
D)
(5m + n)(p –5)(p –6)
Solve the equation.
175)
m(4m –23) = –15
175)
A)
4
3, 5
B)
–3
4, 5
C)
3
4, 5
D)
3
4, –5
C
176)
The length of a rectangular flower bed is 11 ft. less than 3 times its width. The area of the bed is 20
ft2. Find the dimensions of the flower bed.
176)
A)
5 ft by 1 ft
B)
3 ft by 4 ft
C)
5 ft by 4 ft
D)
3 ft by 3 ft
C
Factor out the greatest common factor.
177)
5x2+35x
177)
A)
5x(x +7)
B)
5x(x +35)
C)
x(5x +35)
D)
5x2(x +7)
A
36
D
Solve the problem.
178)
A triangle has a base of length 3x + 1 and a height of x + 6 and has an area of 45 square units. Find
the
base and height. (A =1
2bh)
178)
A)
base = 10 units; height = 9 units
B)
base = 3 units; height = 30 units
C)
base = 3 units; height = 15 units
D)
base = 9 units; height = 5 units
Factor completely.
179)
12x2+24x +9
179)
A)
3(2x +1)(2x –3)
B)
3(2x +1)(2x +3)
C)
(2x +1)(2x +3)
D)
3(2x + 1)(2x +9)
B
Solve the problem.
180)
What pair of integers would be used to rewrite the middle term when factoring 14x2–38x +20 by
grouping?
180)
A)
10, 28
B)
–14, 20
C)
14, –20
D)
–10, –28
D
Factor the polynomial completely.
181)
64s3+ 1
181)
A)
(4s + 1)(16s2+ 1)
B)
(4s – 1)(16s2+ 4s + 1)
C)
(64s + 1)(s2– 4s + 1)
D)
(4s + 1)(16s2– 4s + 1)
D
37
A
Factor completely. If the polynomial is prime, say so.
182)
25m2–40m +7
182)
A)
(5m –7)(5m – 1)
B)
(5m –7)(5m + 1)
C)
(5m – 1)(5m –7)
D)
(5m +7)(5m – 1)
Factor by grouping.
183)
r3+r2+2r +2
183)
A)
(r2+2)(r –2)
B)
(r2+2)(r + 1)
C)
(r2+2)(r +2)
D)
(r2+ 1)(r +2)
B
184)
18a3– 15a2b + 12ab2– 10b3
184)
A)
(3a2– 2b2)(6a + 5b)
B)
(18a2+ 2b2)(a – 5b)
C)
(3a2+ 2b)(6a – 5b)
D)
(3a2+ 2b2)(6a – 5b)
D
Solve the problem.
185)
A triangle has a base of length 2x + 3 and a height of x + 3 and has an area of 27 square units. Find
the
base and height. (A =1
2bh)
185)
A)
base = 18 units; height = 3 units
B)
base = 9 units; height = 6 units
C)
base = 9 units; height = 3 units
D)
base = 3 units; height = 9 unit
B
38
A
Solve the equation.
186)
3k2– 23k – 8 = 0
186)
A)
–1
3, 3
B)
1
23, –1
3
C)
{–3, 8}
D)
–1
3, 8
Factor by grouping.
187)
20 – 9x +x2
187)
A)
(x + 5)(x – 4)
B)
(x + 5)(x + 4)
C)
(x – 5)(x + 4)
D)
(x – 5)(x – 4)
Factor completely.
188)
x2+ 5x – 14
188)
A)
Prime
B)
(x – 7)(x + 2)
C)
(x – 7)(x + 1)
D)
(x + 7)(x – 2)
Factor the polynomial completely.
189)
64a3– 27b3
189)
A)
(64a – 3b)(a2+ 12ab + 9b2)
B)
(4a + 3b2)(16a2– 12ab + 9b2)
C)
(4a – 3b)(16a2+ 12ab + 9b2)
D)
(4a – 3b)(16a2+ 9b2)
Factor completely. If the polynomial is prime, say so.
190)
x2+ 47x + 48
190)
A)
(x + 48)(x – 1)
B)
(x + 12)(x – 4)
C)
(x – 12)(x + 4)
D)
Prime
39
Find the greatest common factor of the numbers.
191)
20, 32
191)
A)
52
B)
5
C)
2
D)
4
Solve the problem.
192)
The table shows the population of a city over the past five years.
Year Population (in millions of people)
1995 65
1996 65.5
1997 67
1998 69
1999 71.5
We used this data to develop the quadratic equation y = .373x2+ .165x + 65, which models the
population of the city y in millions in the year x, where x = 0 represents 1995, x = 1 represents 1996,
and so on. Use the model to find the estimated population in the year 1997.
192)
A)
65,538,000
B)
1,490,000,000,000
C)
66,822,000
D)
1,490,000
C
Factor completely.
193)
49x2+ 28xy + 4y2
193)
A)
(7x – 2y)2
B)
Prime
C)
(7x + 2y)(7x – 2y)
D)
(7x + 2y)2
D
Factor by grouping.
194)
r2–7r + rt –7t
194)
A)
(r –7)(r – t)
B)
(r +7)(r – t)
C)
rt(r –7)
D)
(r –7)(r + t)
D
40
D
Solve the problem.
195)
A rectangle has a length of x + 2 and a width of x – 2, and has an area of 60 square units. Find the
length and width of the rectangle. (A = LW)
195)
A)
width = 3 units; length = 20 units
B)
width = 5 units; length = 12 units
C)
width = 6 units; length = 10 units
D)
width = 4 units; length = 15 units
Find the greatest common factor of the numbers.
196)
10, 30, 40, 45
196)
A)
5
B)
2
C)
1
D)
10
197)
64k2– 25 = 0
197)
A)
5
8, –5
8
B)
8
5, 0
C)
{5, 0}
D)
8
5, –8
5
198)
x2– x – 35
198)
A)
(x – 5)(x + 7)
B)
(x + 5)(x – 7)
C)
(x – 35)(x + 1)
D)
Prime
199)
112
199)
A)
242
B)
121
C)
22
D)
13
Solve the problem.
200)
Find three consecutive integers such that the sum of the squares of the smaller two is equal to the
square of the largest.
200)
A)
–3, –4, –5
B)
–1, 0, 1
C)
3, 4, 5
D)
–1, 0, 1 or 3, 4, 5
201)
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find
the length of the ladder if the length is 5 feet more than its distance from the wall.
201)
A)
20 ft
B)
25 ft
C)
15 ft
D)
30 ft
202)
8a4– 98b2
202)
A)
2(2a2+ 7b)2
B)
2(2a2+ 7b)(2a2– 7b)
C)
2(2a2– 7b)2
D)
Prime
203)
9y4– 64
203)
A)
(3y2– 8)2
B)
(3y2+ 8)(3y2– 8)
C)
(3y2+ 8)2
D)
Prime
Solve the problem.
204)
A triangle has a base of length x + 2 and a height of x + 8 and has an area of 36 square units. Find
the base and height. (A =1
2bh)
204)
A)
base = 6 units; height = 6 units
B)
base = 6 units; height = 12 units
C)
base = 8 units; height = 9 units
D)
base = 4 units; height = 9 units
42
Factor completely.
205)
3x2– 24x + 45
205)
A)
Prime
B)
3(x – 15)(x + 1)
C)
3(x – 3)(x – 5)
D)
(3x – 9)(x – 5)
Solve the equation.
206)
25c3– 35c2+ 10c = 0
206)
A)
2
5, 1, 0
B)
2
5, 1
C)
{0}
D)
2
5, –2
5
Factor completely.
207)
21m3n3–4m2n4– mn5
207)
A)
mn3(7m – n)(3m + n)
B)
mn3(3m – n)(7m + n)
C)
mn3(3m + n)(7m – n)
D)
n3(3m – n)(7m + n)
208)
21m4, 189m7, 441m5
208)
A)
21m3
B)
21m4
C)
3969m3
D)
189m4
209)
The length of a rectangular frame is 6 cm more than the width. The area inside the frame is 112
square cm. Find the width of the frame.
209)
A)
10 cm
B)
8 cm
C)
14 cm
D)
20 cm
Factor by grouping.
210)
6x2+ 13xt + 6t2
210)
A)
(2x – 3t)(3x – 2t)
B)
(6x + 3t)(x + 2t)
C)
(2x + 3t)(3x + 2t)
D)
Prime
Solve the equation.
211)
3y(5y +9) =6
211)
A)
1
5
B)
–1
5, 2
C)
1
5, –2
D)
1
5, 2
C
Factor the binomial completely. If it is prime, say so.
212)
294x2–384
212)
A)
(42x + 48)(7x – 8)
B)
6(7x – 8)2
C)
6(7x + 8)(7x – 8)
D)
(7x + 8)(42x – 48)
C
Factor completely.
213)
u2– 4uv – 45v2= (u + 5v)( )
213)
A)
u – 9
B)
u + 9v2
C)
u + 9v
D)
u – 9v
D
Factor the polynomial completely.
214)
729c3+ 1000
214)
A)
(729c + 10)(c2– 90c + 100)
B)
(9c + 10)(81c2– 90c + 100)
C)
(9c – 10)(81c2+ 90c + 100)
D)
(9c + 10)(81c2+ 100)
B
44
C
Factor completely. If the polynomial cannot be factored, write prime.
215)
x2+ 13x + 14
215)
A)
(x + 7)(x – 2)
B)
(x + 14)(x – 1)
C)
(x – 7)(x + 2)
D)
Prime
Solve the problem.
216)
A parallelogram has a base of length 3x + 1 and a height of x + 1 and has an area of 96 square units.
Find the base and height of the parallelogram. (A = bh)
216)
A)
height = 8 units; base = 12 units
B)
height = 2 units; base = 48 units
C)
height = 6 units; base = 16 units
D)
height = 4 units; base = 24 units
Complete the factoring.
217)
x2– 3x – 28 = (x + 4)( )
217)
A)
–x – 7
B)
7– x
C)
x + 7
D)
x – 7
218)
48x8y8=6x5y6( )
218)
A)
288x4y3
B)
288x3y2
C)
8x3y2
D)
8xy2
219)
9x2– 9x – 54
219)
A)
Prime
B)
9(x – 2)(x + 3)
C)
(9x + 18)(x – 3)
D)
9(x + 2)(x – 3)
Factor by grouping.
220)
10x2+ 8xy + 15xy + 12y2
220)
A)
(2x + 3)(5x + 4)
B)
(10x + 3y)(x + 4y)
C)
(2x – 3y)(5x + 4y)
D)
(2x + 3y)(5x + 4y)
Solve the equation.
221)
(x + 4)(x2+ 6x – 27) = 0
221)
A)
{–4, –9, 3}
B)
{–4}
C)
{4}
D)
{4, 9, –3}
A
Solve the problem. Round to the nearest tenth, if necessary.
222)
If an object is thrown upward with an initial velocity of 128 ft/sec, its height after t sec is given by
h =128t – 16t2. Find the maximum height attained by the object. (The object will attain maximum
height exactly at the halfway point in terms of the time t, where t = 0 is at the beginning of the
object’s flight, and the final time is when the object hits the ground.)
222)
A)
128 ft
B)
256 ft
C)
240 ft
D)
112 ft
B
223)
Product: 160 Sum: –28
223)
A)
–20 and –8
B)
–20 and 8
C)
20 and 8
D)
20 and –8
A
Factor by grouping.
224)
12x2– 25xt + 12t2
224)
A)
(12x – 3t)(x – 4t)
B)
(4x + 3t)(3x + 4t)
C)
(4x – 3t)(3x – 4t)
D)
Prime
C
46
D
225)
10z2– 11z – 6
225)
A)
(2z – 3)(5z + 2)
B)
(10z – 3)(z + 2)
C)
(2z + 3)(5z – 2)
D)
Prime
226)
Below is a diagram of a water slide. The slide is 17 ft long. The ladder leading to the slide is 13 ft
long. How far is it from the end of the slide to the foot of the ladder? Round approximations to the
nearest tenth.
13 ft 17 ft
?
226)
A)
15 ft
B)
60 ft
C)
11 ft
D)
5.5 ft
D)
Solve the equation.
227)
(x – 7)(56x2+ 85x + 24) = 0
227)
A)
{7}
B)
7, –3
8, –8
7
C)
–7
8, –8
7
D)
7, 3
8, 8
7
D)
Factor by grouping.
228)
x2+6x + xy +6y
228)
A)
(x +6)(x + y)
B)
(x –6)(x + y)
C)
(x –6)(x – y)
D)
(x +6)(x – y)
D)
47
D)
Solve the problem.
229)
The height of a box is 4 inches. Its length is 5 inches more than its width. Find the length if the
volume is 200 cubic inches.
229)
A)
5 in.
B)
50 in.
C)
10 in.
D)
4 in.
Factor completely.
230)
x2+ 2xy – 8y2= (x + 4y)( )
230)
A)
x – 2y2
B)
x – 2y
C)
x + 2y
D)
x + y
Complete the factoring.
231)
x2– 9x + 14 = (x – 7)( )
231)
A)
7– x
B)
x + 2
C)
x2+ 7
D)
x – 2
Provide an appropriate response.
232)
Is x10y5 a common factor of –x11y6 and x10y5?
232)
A)
No
B)
Yes
Solve the problem.
233)
Doris has a rectangular fish pond 9 by 14 feet. She wants to put grass in a strip of uniform width
around the pond. She has enough grass seed for 108 square feet. How wide will the strip be?
233)
A)
3 ft
B)
4.5 ft
C)
4 ft
D)
2 ft
Factor the polynomial completely.
234)
t3+ 64
234)
A)
(t – 4)(t2+ 4t + 16)
B)
(t + 4)(t2– 4t + 16)
C)
(t – 64)(t2– 1)
D)
(t + 4)(t2+ 16)
Factor completely.
235)
x4+2x3y –3x2y2
235)
A)
x(x +3y)(x – y)
B)
x2(x –3y)(x – y)
C)
x2(x +3y)(x – y)
D)
x2(x –3y)(x + y)
236)
3x2– 9xy – 12y2=3( )( )
236)
A)
x – 3y, x + 4y
B)
x + y, x – 4y
C)
x +3y, x – 4y
D)
x – y, x + 4y
Factor completely. If the polynomial is prime, say so.
237)
16p4–81q4
237)
A)
(2p +3q)(2p –3q)(4p2–9q2)
B)
(2p +3q)3(2p –3q)
C)
(2p +3q)(2p +3q)(4p2–9q2)
D)
(2p +3q)(2p –3q)(4p2+9q2)
Factor completely. If the polynomial cannot be factored, write prime.
238)
x2+ 8x – 33
238)
A)
(x – 11)(x + 1)
B)
(x – 11)(x + 3)
C)
(x + 11)(x – 3)
D)
Prime
49
Solve the problem. Round to the nearest tenth, if necessary.
239)
If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per second,
then its height h after t seconds is given by the equation h = –16t2+80t +96. After how many
seconds does the object hit the ground?
239)
A)
5.0 sec
B)
3.0 sec
C)
6 sec
D)
11 sec
240)
5x5– 40x4– 45x3
240)
A)
5x3(x – 9)(x + 1)
B)
x3(x – 9)(5x + 5)
C)
53(x2– 8x – 9)
D)
x3(5x – 45)(x + 1)
241)
25a6b4+ 30a3b2+ 9
241)
A)
Prime
B)
(5a3b2+ 3)(5a3b2– 3)
C)
(5a3b2– 3)2
D)
(5a3b2+ 3)2
Solve the equation.
242)
12d2+ 42d + 18 = 0
242)
A)
3, 1
2
B)
–1
3, –1
2
C)
1
3, 2
D)
–3, –1
2
50
Factor out the greatest common factor.
243)
12m2– 17r3
243)
A)
2(6m2+ 8r3)
B)
m2(12 – 17m)
C)
3(4m2– 5r3)
D)
No common factor (except 1)
Solve the equation.
244)
6x(x +1) = (2x +8)(x +1)
244)
A)
{–1, 4}
B)
{1, 2}
C)
{1, 4}
D)
{–1, 2}
Factor completely. If the polynomial is prime, say so.
245)
36 –4r –9t +rt
245)
A)
(9 –r)(4–t)
B)
(9 +r)(4–t)
C)
(9 +r)(4+t)
D)
(9 –r)(4+t)
Solve the problem.
246)
Find three consecutive odd integers such that the sum of all three is 36 less than the product of the
smaller two.
246)
A)
5, 7, 9
B)
7, 9, 11, or –6, –4, –2
C)
–6, –4, –2
D)
7, 9, 11
Solve the equation.
247)
(x – 8)(x + 9) = 0
247)
A)
{8, 9}
B)
{8, –8, 9, –9}
C)
{8, –9}
D)
{–8, 9}
51
Solve the problem.
248)
A boat travels 8 miles south and then 10 miles east. How far is the boat from its starting point?
Round approximations to the nearest tenth.
South
8 mi East ––10 mi–>
248)
A)
12.8 mi
B)
6.4 mi
C)
82 mi
D)
9 mi
Factor completely. If the polynomial is prime, say so.
249)
5x4y2+2x4y –6x3y3
249)
A)
x3(5xy2+2xy –6y3)
B)
x3y(5xy +2x –6y2)
C)
x3y(5xy –2x +6y2)
D)
x3(5xy –2x –6y2)
Factor the binomial completely. If it is prime, say so.
250)
x4–256
250)
A)
(x2–16)(x +4)(x –4)
B)
(x +4)2(x –4)2
C)
(x2+16)(x +4)(x –4)
D)
Prime
Solve the problem. Round to the nearest tenth, if necessary.
251)
If an object is propelled upward from a height of 80 feet at an initial velocity of 64 feet per second,
then its height after t seconds is given by the equation h = –16t2+ 64t + 80, where h is in feet. After
how many seconds will the object reach a height of 144 feet?
251)
A)
4 sec
B)
8 sec
C)
2 sec
D)
1 sec
Solve the problem.
252)
A square piece of cardboard is to be formed into an open–topped box by cutting 3 inch squares
from the corners and folding up the sides. The volume of the resulting box is given by the formula
V =3(x –6)2, where x is the original length of each side of the piece of cardboard. What is the
volume of the box if the original length of each side of the piece of cardboard is 16 inches?
252)
A)
30 in.3
B)
100in.3
C)
300in.3
D)
768in.3
Factor by grouping.
253)
20z4+ 7z2– 6
253)
A)
(4z2+ 3)(5z2– 2)
B)
(4z4+ 3)(5z – 2)
C)
(5z4+ 2)(4z – 3)
D)
(5z2+ 2)(4z2– 3)
Factor completely.
254)
8x2–48x +72
254)
A)
8(x –3)2
B)
8(x +3)2
C)
(8x –48)2
D)
Prime
Solve the problem.
255)
A painter leans a ladder against one wall of a house. The ladder is 27 ft long. The base of the ladder
is 20 ft from the house. How high is the wall? Round approximations to the nearest tenth.
?27 ft
20 ft
255)
A)
23.5 ft
B)
18.1 ft
C)
9.1 ft
D)
164.5 ft
256)
A long–distance runner runs 6 miles south and then 9 miles east. How far is the runner from the
starting point? Round approximations to the nearest tenth.
South
6 mi East ––9 mi–>
256)
A)
58.5 mi
B)
5.4 mi
C)
7.5 mi
D)
10.8 mi
54
Answer Key
Testname: C6
Answer Key
Testname: C6
56
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6