Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the graph that matches the function.
1)
f(x) = x2+ 3x – 28
1)
A)
B)
C)
D)
1
2)
f(x) =-2x(x + 1)2
2)
A)
B)
C)
D)
2
3)
f(x) = x3+ 9x2– 36x
3)
A)
B)
C)
D)
3
4)
f(x) = (x + 2)(x – 1)
4)
A)
B)
C)
D)
4
5)
f(x) =3x(x + 1)(x + 2)
5)
A)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
6)
A student is trying to solve the equation (x + 2)(x – 4) =3. The student set x + 2 = 3 and
x – 4 = 3 and found that the two solutions were x =1, x =7. The student then checked her
results by plugging in her solutions into the original equation and found that they do not
work. How would you advise her?
6)
7)
What is the difference between a trinomial of degree 2 and a quadratic equation?
7)
8)
Explain the error in the following: x2+ 16 = (x + 4)(x – 4)
8)
9)
A trinomial in z is factored as (z + a)(z + b). If the coefficient of the last term of the trinomial
is positive, what must be true of a and b?
9)
10)
Give an example of three numbers whose greatest common factor is 6.
10)
11)
Explain why x2+ 2x + 16 is prime.
11)
12)
What steps would you take to factor x2– 6x + 8 ?
12)
5
13)
How would you solve the equation (4x + 9)(6x – 3)(5x – 6) = 0? How many equations would
you need to solve it? What are their solutions?
13)
14)
What steps would you take to factor x2+ 12x + 27 ?
14)
15)
Explain two different ways to begin factoring the binomial x6–y6.
15)
16)
The FOIL method can be used to show that (5x + 10)(x – 9)=5x2– 35x – 90.If you were
asked to factor the expression 5x2– 35x – 90 completely, why would it be incorrect to give
(5x + 10)(x – 9) as your answer?
16)
17)
Write an equation whose solutions are 2 and –3.
17)
18)
What is wrong with the following factorization?
9s6t3+3s4t4=3s4t3(3s3+ t)
18)
19)
The binomial 9x2+ 36 is the sum of two squares that can be factored. How is this possible?
19)
20)
What is wrong with the following factorization?
–8u –16u2+12u3v –16uv = –4uv(2 + 4u – 3u2+ 4)
20)
21)
4x3y2(6x – 3y + 12) = 24x4y2– 12x3y3+ 48x3y2.
However, 4x3y2(6x – 3y + 12) is not the correct prime factorization of
24x4y2 – 12x3y3 + 48x3y2. Why not?
21)
22)
Write a problem in which the quadratic equation x(x + 3) = 108 must be solved in order to
solve the problem.
22)
23)
What is wrong with solving x2= 6x by dividing both sides of the equation by x?
23)
24)
Explain the error in the following: x2+ 2x – 15 = (x – 5)(x + 3).
24)
25)
Explain the error in the following: 25x2– 100 = (5x + 10)(5x – 10).
25)
26)
Explain the error in the following: 10x2– 90 = (x + 3)(x – 3).
26)
27)
Explain the error in the following: 25x2+ 10x – 4 =(5x + 2)2
27)
28)
How can you determine if your factorization of a polynomial is correct?
28)
29)
Will there always be two solutions when the zero–factor theorem is used to solve a
quadratic equation? Why or why not?
29)
6
30)
Explain how to construct an equation that has four solutions.
30)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the formula B = P 1 +r
nnt, which is used to calculate the final balance of an investment or a loan after being
compounded. Following is a list of what each variable represents:
B represents the final balance.
P represents the principal.
r represents the annual percentage rate.
t represents the time in years in which the principal is compounded.
n represents the number of times the principal is compounded in a year.
31)
Sheila invests $20,000 in an account that is compounded semiannually. If, after one year, her
balance is $22,472, what is the interest rate of the account?
31)
A)
13%
B)
10%
C)
11%
D)
12%
Factor completely.
32)
r2+ 3r –4
32)
A)
(r –4)(r + 3)
B)
(r –4)(r +1)
C)
(r +4)(r –1)
D)
Prime
Factor out the GCF.
33)
7z –56
33)
A)
7(z –56)
B)
7(z +8)
C)
8(z –7)
D)
7(z –8)
Factor completely.
34)
9x2– 9x – 54
34)
A)
9(x – 2)(x + 3)
B)
9(x + 2)(x – 3)
C)
(9x + 18)(x – 3)
D)
Prime
Factor by grouping.
35)
nw +w+n+ 1
35)
A)
(n + 1)(w+n)
B)
(nw + 1)(w+n)
C)
(n + 1)(w+ 1)
D)
(nw +n)(w+ 1)
Factor completely.
36)
4x2–9x +4
36)
A)
(4x –4)(x – 1)
B)
(4x – 1)(x –4)
C)
(2x –4)(2x – 1)
D)
Prime
Factor out the GCF.
37)
48a9b3c8– 96a7bc6+ 96a3b2c3
37)
A)
48a3(1a6b3c8– 2a4bc6+ 2b2c3)
B)
48a9b3c8(1 – 2a7bc6+ 2a3b2c3)
C)
48a3bc3(1a6b2c5– 2a4c3+ 2b)
D)
48(1a9b3c8– 2a7bc6+ 2a3b2c3)
Factor the trinomial containing two variables.
38)
a2+28ab +27b2
38)
A)
(a +27b)(a + b)
B)
(ab +27)(ab + 1)
C)
(a + b)(27a + b)
D)
(a +28b)(a + b)
Factor by grouping.
39)
xa –xb –5a +5b
39)
A)
(x – a)(5– b)
B)
(a – b)(x+5)
C)
(a – b)(x–5)
D)
(a –5)(x– b)
7
Solve.
40)
The final balance in an account that earns simple interest is the sum of the principal and the
product of the principal, interest rate, and time. Write an expression for the final balance in an
account which earns simple interest at a rate of 6%. Then write the expression in factored form.
40)
A)
p + 0.06pt = p(0.06+ t)
B)
p + 0.06pt = p(1 + 0.06t)
C)
p + 0.06pt = p(1 + 0.06pt)
D)
p + 0.06pt = 0.06p(1 + t)
Factor completely.
41)
8ab +24b –4a –12
41)
A)
4(a + 1)(2b –3)
B)
(a +3)(8b – 1)
C)
4(a +3)(2b – 1)
D)
4(a –3)(2b + 1)
Find the GCF.
42)
21m4n8, 12m2n6, 9m6n2
42)
A)
m2n2
B)
3m6n8
C)
3m2n2
D)
9m6n8
Find all natural–number values of b that make the trinomial factorable.
43)
x2+ bx +28
43)
A)
11, 16, 29
B)
11, 16
C)
1, 14, 28
D)
16, 29
Factor the difference of squares.
44)
36(x + y)2–25z2
44)
A)
(6x +6y +25z)(6x +6y –25z)
B)
(6x + y +5z)(6x + y –5z)
C)
(6x +6y +5z)(6x –6y –5z)
D)
(6x +6y +5z)(6x +6y –5z)
Use a graphing calculator to determine the x–intercepts.
45)
f(x) =15x2+ 22x + 8
45)
A)
2
3, 0 , – 4
5, 0
B)
– 2
15, 0 , – 1
2, 0
C)
2
3, 0 , 4
5, 0
D)
– 2
3, 0 , – 4
5, 0
Factor by grouping.
46)
5a2– 31ab – 28b2
46)
A)
(5a + 4b)(a – 7b)
B)
(5a + b)(a – 28b)
C)
(4a + 5b)(a – 7b)
D)
(5a – 7b)(a + 4b)
Factor completely.
47)
7pa +7aq –7pw –7wq
47)
A)
7(a – q)(p +w)
B)
7(a +w)(p – q)
C)
7(a –w)(p + q)
D)
7(a + p)(q –w)
Use a graphing calculator to verify that the factoring is correct. If it is not, write the correct factored form.
48)
2x5+12x4=2x4(x +6)
48)
A)
It is correct.
B)
Correct form: x4(2x +12)
C)
Correct form: 2x5(x +6)
D)
Correct form: 2x4(x +12)
8
Solve.
49)
Find the length of each side of the right triangle shown.
m2m + 1
m + 7
49)
A)
21, 25, 28
B)
5, 12, 13
C)
10, 17, 21
D)
8, 15, 17
Factor the trinomial containing two variables.
50)
x2+ 4xy – 140y2
50)
A)
(x – y)(x + 10y)
B)
(x – 14y)(x + 10y)
C)
(x + 14y)(x – 10y)
D)
(x – 14y)(x + y)
Solve.
51)
2k2=-9k –9
51)
A)
3, 3
2
B)
– 3
2, -3
C)
-3, -6
D)
3, – 3
2
Factor out the GCF.
52)
x9y8–x9y7+x7y5–x6y5
52)
A)
x6y5(x2y3–x2y2+ xy – 1)
B)
x6y5(x3y3–x3y2+ x – 1)
C)
x5y5(x3y3+ x3y2+ x + 1)
D)
x6y5(x3y3–x2y2+ x – 1)
Find all natural–number values of b that make the trinomial factorable.
53)
x2+ bx –91
53)
A)
6, 90
B)
20, 92
C)
6
D)
90
Factor by grouping.
54)
x3+8x2–10x –80
54)
A)
(x +8)(x2–10)
B)
(x –8)(x2–10)
C)
(x2+8)(x –10)
D)
(x +8)(x3–10x)
Factor the difference of squares.
55)
3t2–3a2
55)
A)
3(t + a)(t– a)
B)
(3t + a)(3t – a)
C)
3ta(t+ a)(t– a)
D)
3(t – a)2
Factor by grouping.
56)
uv –7u + 5v –35
56)
A)
(v –7)(u + 5)
B)
(v +7)(u – 5)
C)
(v – 5)(u +7)
D)
5u(v –7)
Factor the perfect square.
57)
x2+ 12x + 36
57)
A)
(x – 6)2
B)
(x + 6)2
C)
(x + 6)(x – 6)
D)
Prime
9
Solve.
58)
If an object is propelled upward from a height of 128 feet at an initial velocity of 112 feet per
second, then its height, h, after t seconds is given by the equation h = -16t2 + 112t + 128, where h is
in feet. After how many seconds does the object hit the ground? (Round your answer to the nearest
tenth, if necessary.)
58)
A)
8 sec
B)
4.0 sec
C)
11 sec
D)
7.0 sec
Factor completely.
59)
x2– 4x – 96
59)
A)
(x – 8)(x + 1)
B)
(x – 8)(x + 12)
C)
(x + 8)(x – 12)
D)
Prime
60)
4x2– 9x – 9
60)
A)
(4x – 3)(x + 3)
B)
(3x + 4)(x – 3)
C)
(4x + 1)(x – 9)
D)
(4x + 3)(x – 3)
Find the natural number b that makes the expression a perfect square trinomial.
61)
x2+6x + b
61)
A)
6
B)
3
C)
9
D)
36
Factor by grouping.
62)
5y +5a –y2–ya
62)
A)
(y +a)(5–y)
B)
(y +a)(5–a)
C)
(y –a)(5–y)
D)
(y –a)(5+y)
Write a polynomial equation in standard form with the given solutions.
63)
-7, 8
63)
A)
x2– 15x + 56 = 0
B)
x2+ 15x + 56 = 0
C)
x2– x – 56 = 0
D)
x2+ x – 56 = 0
Provide an appropriate response.
64)
Is x4y8z6 a common factor of x5y9z7and –x4y9z6?
64)
A)
Yes
B)
No
Factor completely.
65)
64m2n –64mn +40m2–40m
65)
A)
8m(m –5)(8n + 1)
B)
8m(m – 1)(8n +5)
C)
8m(m + 1)(8n –5)
D)
8(m2– 1)(8n +5m)
Factor using substitution.
66)
t4–29t2+100
66)
A)
(t –2)(t +2)(t –5)(t +5)
B)
t2(t –4)(t –25)
C)
(t – 2)2(t – 5)2
D)
(t2+4)(t2+25)
Solve.
67)
20y2+ 23y + 6 = 0
67)
A)
–3
20, –1
3
B)
3
4, –2
5
C)
3
4, 2
5
D)
–3
4, –2
5
10
Factor using substitution.
68)
3(y + 6)2– 11(y + 6) – 4
68)
A)
(3y + 1)(y + 38)
B)
(3y + 19)(y + 2)
C)
(3y + 14)(y + 7)
D)
(3y + 17)(y + 10)
Use a graphing calculator to solve the equation.
69)
5x2– 11x =12
69)
A)
– 4
5, 0
B)
– 4
5, –3
C)
– 4
5, 3
D)
– 4
5, 1
Solve.
70)
3x3+28x2= –49x
70)
A)
7, 7
3
B)
–7, –7
3, 0
C)
0, 7, 7
3
D)
–7, –7
3
71)
2k2+25 =-15k
71)
A)
-5, -10
B)
– 5
2, -5
C)
5, – 5
2
D)
5, 5
2
Factor by grouping.
72)
2s2+10s– as–5a
72)
A)
(s– a)(2s+5)
B)
(s–5)(2s + a)
C)
(s+2)(5s – a)
D)
(s+5)(2s – a)
Factor out the GCF.
73)
t(6– m) + s(6– m)
73)
A)
t(6– m) + s
B)
(t + s)(6– m)
C)
(t – s)(6– m)
D)
No common factor
Solve.
74)
(x –5)(5x + 15) = 0
74)
A)
-3 , 5
B)
–1
5, 1
3
C)
–1
3, 1
5
D)
–5, 3
Factor completely.
75)
36z8+ 48z5+ 16z2
75)
A)
4(3z6+ 2)(3z2+ 2)
B)
4z2(3z3– 2)(3z3– 2)
C)
4z2(3z3+ 2)(3z3+ 2)
D)
(3z4+ 3)(3z4+ 2)
Factor the difference of cubes.
76)
m3– 125n3
76)
A)
(m + 5n)(m2– 5mn + 25n2)
B)
(m + 25n)(m2+ 5mn – 5n2)
C)
(m – 5n)3
D)
(m – 5n)(m2+ 5mn + 25n2)
Factor out the GCF.
77)
2s6+8s3
77)
A)
2(s6+ 4s3)
B)
2s3(s3+ 4)
C)
6(s3+ 4s)
D)
s3(2s3+8)
11
Factor the perfect square.
78)
x2+ 14xy + 49y2
78)
A)
(x + 7y)2
B)
(x + 7y)(x – 7y)
C)
(x – 7y)2
D)
Prime
Solve.
79)
Find the length of each side of the right triangle shown.
x- 16 x
x – 2
79)
A)
12, 26, 28
B)
34, 48, 50
C)
15, 36, 39
D)
10, 24, 26
80)
y2+ 11y =-24
80)
A)
3, 8
B)
-8, -3
C)
-8, 3
D)
8, -3
Factor the difference of squares.
81)
25a2–b2
81)
A)
(5a + b)(5a – b)
B)
(a +5b)(a –5b)
C)
(5a – b)2
D)
(5ab + 1)(5ab – 1)
Factor completely.
82)
15xy +45x –3y –9
82)
A)
(3y +3)(5x – 1)
B)
3(y –3)(5x + 1)
C)
(y +3)(15x –3)
D)
3(y +3)(5x – 1)
Factor the difference of cubes.
83)
x3– 343
83)
A)
(x – 7)3
B)
(x + 7)(x2– 7x + 49)
C)
(x – 7)(x2+ 7x + 49)
D)
Prime
Use a graphing calculator to determine the x–intercepts.
84)
f(x) =25x2– 36
84)
A)
(6, 0), (0, 0)
B)
6
5, 0 , – 6
5, 0
C)
5
6, 0 , (0, 0)
D)
– 5
6, 0 , 5
6, 0
Factor completely.
85)
x2+ 3x – 40
85)
A)
(x – 8)(x + 1)
B)
(x + 8)(x – 5)
C)
(x – 8)(x + 5)
D)
Prime
Use a graphing calculator to solve the equation.
86)
x3+ 7x2=-6x
86)
A)
-6, -1
B)
0, 1, 6
C)
0, -6, 1
D)
0, -6, -1
Factor completely.
87)
20z2– 3z – 9
87)
A)
(4z – 3)(5z + 3)
B)
(20z + 1)(z – 9)
C)
(20z – 3)(z + 3)
D)
(4z + 3)(5z – 3)
12
Solve.
88)
(3y + 23)(3y + 26) = 0
88)
A)
–3
20, –3
26
B)
20, 23
C)
–23
3, –26
3
D)
23
3, 26
3
Factor by grouping.
89)
sn + tn+ sw+ tw
89)
A)
(s +w)(n+ t)
B)
(s + t)(n+ t)
C)
(s + t)(n+w)
D)
(s +n)(t +w)
Factor the sum of cubes.
90)
729p3+ 1
90)
A)
(9p + 1)(81p2– 9p + 1)
B)
(9p + 1)(81p2+ 1)
C)
(9p – 1)(81p2+ 9p + 1)
D)
(729p + 1)(p2– 9p + 1)
Find the GCF.
91)
10m5, 40m9
91)
A)
400m4
B)
10m5
C)
10m4
D)
40m5
Factor using substitution.
92)
2x4– 13x2+ 18
92)
A)
(2x2+ 9)(2x2– 9)
B)
(x2– 2)(2x2– 9)
C)
(9 – 2x2)(2x2– 9)
D)
(x2+ 2)(2x2– 9)
Solve.
93)
If an object is propelled upward from a height of 80 feet at an initial velocity of 64 feet per second,
then its height, h, 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? (Round your answer to the
nearest tenth, if necessary.)
93)
A)
1 sec
B)
8 sec
C)
2 sec
D)
4 sec
Find all natural–number values of b that make the trinomial factorable.
94)
x2+ bx +10
94)
A)
11
B)
7, 11
C)
7, 10
D)
7
Write a polynomial equation in standard form with the given solutions.
95)
-5, -9
95)
A)
x2–4x –45 = 0
B)
x2+14x +45 = 0
C)
x2+ 4x +45 = 0
D)
x2– 14x + 45 = 0
Solve.
96)
(4y – 8)2(y + 8)2= 0
96)
A)
–2, 8
B)
1
2, -8
C)
2, 0
D)
2, -8
13
Factor out the GCF.
97)
t10 –8t6
97)
A)
t6(t4+8)
B)
t6(t4–8)
C)
t(t9–8t5)
D)
t4(t6–8)
Factor by grouping.
98)
12c3–2c2d +54cd2–9d3
98)
A)
(6c +9d)(2c2–d2)
B)
(6c +9d2)(2c2– d)
C)
(6c –d2)(2c2+9d)
D)
(6c – d)(2c2+9d2)
Factor out the GCF.
99)
–16u –32u2+24u3v –32uv
99)
A)
–16u(1 + 2u –u2v + 2v)
B)
–8u(2 + 4u – 3u2v + 4v)
C)
–8uv(2 + 4u – 3u2+ 4)
D)
–8(2u + 4u2– 3u3v + 4uv)
Solve.
100)
Find the length of each side of the right triangle shown.
xx + 6
x + 3
100)
A)
12, 15, 18
B)
12, 16, 20
C)
9, 12, 15
D)
6, 8, 10
Factor the trinomial containing two variables.
101)
u2– 3uv – 40v2
101)
A)
(u – 5v)(u + 8v)
B)
(u – v)(u + 8v)
C)
(u + 5v)(u – 8v)
D)
(u – 5v)(u + v)
Find the x–intercepts and then sketch the graph.
102)
f(x) =x2–9
102)
14
A)
(-3, 0)
B)
(-3, 0), (3, 0)
C)
(3, 0)
D)
(0, 0), (3, 0)
Factor by grouping.
103)
x3+3x2+6x +18
103)
A)
(x +3x)(x2+6)
B)
(x –3)(x3+6)
C)
(x +3)(x2+6)
D)
(x +6)(x2+3)
Find the GCF.
104)
s4t5, s2t7
104)
A)
s4t5
B)
s2t2
C)
s2t5
D)
s6t7
Factor the difference of squares.
105)
16 –x4
105)
A)
(2 +x2)(2+x)(2–x)
B)
(2 + x)2(2 – x)2
C)
(4 +x2)(2+x)(2–x)
D)
(4 +x2)(4–x2)
Factor the perfect square.
106)
x2– 12x + 144
106)
A)
(x + 12)2
B)
(x – 12)2
C)
(x + 12)(x – 12)
D)
Prime
Find the x–intercepts and then sketch the graph.
15
107)
f(x) = x(x +10)(x –2)
107)
A)
(–10, 0), (0, 0), (1, 0)
B)
(0, 0), (2, 0), (10, 0)
C)
(-2, 0), (0, 0), (10, 0)
D)
(–10, 0), (0, 0), (2, 0)
Factor by grouping.
108)
ra2+rb2–8a2–8b2
108)
A)
(a2+8b2)(r– 1)
B)
(a2+b2)(r–8)
C)
(a2–8)(r+b2)
D)
(a2–b2)(r+8)
16
Solve.
109)
16k2– 64 = 0
109)
A)
1
2, 0
B)
1
2, –1
2
C)
8, 0
D)
2, –2
Factor out the GCF.
110)
m5n3–m4n5
110)
A)
mn(15 –20)
B)
m4n3(m –n2)
C)
m5n3(1 – mn2)
D)
m5n5(m –n2)
111)
2x(3x – 5) + 5(3x – 5)
111)
A)
(2x + 5)(3x – 5)
B)
(2x – 5)(3x + 5)
C)
(6x – 5)(x + 5)
D)
(6x + 5)(x – 5)
Factor completely.
112)
x2+ 35x + 36
112)
A)
(x – 12)(x + 3)
B)
(x + 36)(x – 1)
C)
(x + 12)(x – 3)
D)
Prime
Factor using substitution.
113)
6z6– 5z3– 6
113)
A)
(6z3– 3)(z3+ 2)
B)
(6z3+ 1)(z3– 6)
C)
(2z3+ 3)(3z3– 2)
D)
(2z3– 3)(3z3+ 2)
Factor the sum of cubes.
114)
27k3+m3
114)
A)
(3k + m)(9k2–3km +m2)
B)
(3k + m)(9k2+3km +m2)
C)
(3k + m)(9k2+m2)
D)
(3k + m)(9k2–3km –m2)
Solve.
115)
The distance an object travels after accelerating from an initial velocity is the product of velocity
and the time added to one–half of the product of the acceleration and the square of the time. Write
an expression for the height h of an object t seconds after being fired straight up into the air with an
initial velocity of 288 m/sec. Then write the expression in factored form.
[Note: The acceleration of an object fired vertically upwards is –9.8. m/s2]
115)
A)
288t – 4.9t2= 4.9t(288– t)
B)
288t – 9.8t2=t2(288– 9.8t)
C)
288t – 4.9t2= t(288– 4.9t)
D)
288t – 9.8t2= t(288– 9.8t)
Factor the trinomial containing two variables.
116)
x2+ 5xy – 14y2
116)
A)
(x – 7y)(x + y)
B)
(x – 7y)(x + 2y)
C)
(x – y)(x + 2y)
D)
(x + 7y)(x – 2y)
Factor completely.
117)
49a2– (b2–16b +64)
117)
A)
(7a + b –16)(7a – b +16)
B)
(7a – b + 8)2
C)
(7a + b +8)(7a – b –8)
D)
(7a + b –8)(7a – b +8)
17
Factor out the GCF.
118)
j(k –4) –10(k –4)
118)
A)
–10j (k –4)
B)
(j –10)(k +4)
C)
(j –10)(k –4)
D)
(j +10)(k –4)
Factor the difference of squares.
119)
5x2–245
119)
A)
(5x – 7)(5x + 7)
B)
5(x + 7)2
C)
5(x2– 7)(x2+ 7)
D)
5(x – 7)(x + 7)
Factor completely.
120)
x2– x – 42
120)
A)
(x + 1)(x – 42)
B)
(x + 7)(x – 6)
C)
(x + 6)(x – 7)
D)
Prime
121)
200x6y – 320x3y3+128y5
121)
A)
8y(5x3– 4y2)2
B)
y(40x3– 32y2)(5x3– 4y2)
C)
8y(5x3+ 4y2)(5x3– 4y2)
D)
8(5x3y – 4y2)2
122)
6x3+17x2–3x
122)
A)
x(6x – 1)(x +3)
B)
(6x2– 1)(x +3)
C)
x(6x + 1)(x –3)
D)
Prime
Factor the sum of cubes.
123)
27a6+b3a3
123)
A)
a3(3 + ab)(9–3ab +b2a2)
B)
(3a2+ ba)(9a4–3ba3+b2a2)
C)
a3(3a – b)(9a2+3ab +b2)
D)
a3(3a + b)(9a2–3ab +b2)
Solve.
124)
Find a number such that 2 plus the number is the same as the square of the number.
124)
A)
–2, 1
B)
–1, 2
C)
–1, 1
D)
–2, 2
Factor completely.
125)
x4+x3y – 27x – 27y
125)
A)
(x – 3)(x2+ 3x + 9)(x + y)
B)
(x + 3)(x2 – 3x + 9)(x – y)
C)
(x – 27)(x3+ x + y)
D)
(x + 3)(x2 – 3x + 9)(x + y)
126)
4a3+16a2–20a
126)
A)
4a(a –5)(a +1)
B)
a(4a + 1)(a –20)
C)
4(a2+5)(a –1)
D)
4a(a +5)(a –1)
Solve.
127)
b(b + 18) = 0
127)
A)
1, -18
B)
18, 0
C)
-18, 0
D)
–1, -18
128)
b2+ 11b = 0
128)
A)
1, -11
B)
–1, -11
C)
11, 0
D)
-11, 0
18
Factor the sum of cubes.
129)
x3+t3
129)
A)
(x + t)(x2– xt –t2)
B)
(x + t)(x2+t2)
C)
(x + t)(x2– xt +t2)
D)
(x – t)(x2– xt +t2)
Factor completely.
130)
3a3+3a2–3ab2–3b2
130)
A)
(a + b)(a – b)(3a +3)
B)
(a – b)(3a2+3b2)
C)
(a – b)2(3a +3)
D)
(a2+b2)(3a –3)
Factor by grouping.
131)
8x2+ 10xt + 3t2
131)
A)
prime
B)
(2x – t)(4x – 3t)
C)
(8x + t)(x + 3t)
D)
(2x + t)(4x + 3t)
Solve.
132)
2k2– 5k – 3 = 0
132)
A)
1
5, –1
2
B)
–1
2, 3
C)
–2, 3
D)
–1
2, 2
Find the x–intercepts and then sketch the graph.
133)
f(x) = x2+ 6x – 40
133)
A)
(–10, 0), (1, 0)
B)
(10, 0), (-4, 0)
19
C)
(–10, 0), (4, 0)
D)
(10, 0), (4, 0)
Factor completely.
134)
36x2–12x +1
134)
A)
(36x –1)(x –1)
B)
(6x + 1)2
C)
(6x – 1)2
D)
Prime
135)
10(p + 4)2+ 27(p + 4) + 5
135)
A)
(5p + 5)(2p + 9)
B)
(5p + 25)(2p + 9)
C)
(5p + 1)(2p + 5)
D)
(5p + 21)(2p + 13)
Provide an appropriate response.
136)
What is wrong with the following factoring: 36x2– 9 = (6x – 3)(6x + 3).
136)
A)
The expression is not factorable.
B)
The factored expression should be (6x – 3)2.
C)
It is not completely factored; the factored expression should be 9(2x – 1)(2x + 1).
D)
Nothing is wrong.
Write a polynomial equation in standard form with the given solutions.
137)
-7, 6
137)
A)
x2+ x – 42 = 0
B)
x2+7x +42 = 0
C)
x2–13x +42 = 0
D)
x2– x – 42 = 0
Factor completely.
138)
5u3– 2u2– 25u2v + 10uv
138)
A)
(5u2– 2)(u – 5v)
B)
u(5u – 5)(u – 2v)
C)
u(5u – 2)(u – 5v)
D)
(5u – 5)(u – 2uv)
Solve.
139)
20x(x –5) + 40 =-55(2x – 1) + 15
139)
A)
–3
2, 1
B)
–6, 1
C)
–1, 3
2
D)
–5, 1
2
20
Find all natural–number values of b that make the trinomial factorable.
140)
x2+8x + b
140)
A)
7, 12, 15, 16
B)
4, 5, 6, 7
C)
7, 12, 15
D)
7, 12
Find the natural number b that makes the expression a perfect square trinomial.
141)
25x2–70x + b
141)
A)
49
B)
35
C)
1225
D)
7
Factor completely.
142)
x2– x – 40
142)
A)
(x – 5)(x + 8)
B)
(x – 40)(x + 1)
C)
(x + 5)(x – 8)
D)
Prime
Factor the trinomial containing two variables.
143)
x2– 2xy – 15y2
143)
A)
(x – 5y)(x + 3y)
B)
(x + 5y)(x – 3y)
C)
(x – y)(x + 3y)
D)
(x – 5y)(x + y)
Use a graphing calculator to determine the x–intercepts.
144)
f(x) =6x2– 17x – 3
144)
A)
– 1
6, 0 , 1
17, 0
B)
(–6, 0), (3, 0)
C)
– 1
6, 0 , (3, 0)
D)
– 1
6, 0 , (6, 0)
Factor completely.
145)
7x2– 33x + 20
145)
A)
(7x + 15)(7x – 5)
B)
(x – 4)(7x – 5)
C)
(x + 4)(7x – 5)
D)
(7x – 4)(x – 5)
Provide an appropriate response.
146)
Is x4y2 a common factor of x5y4 and x3y2?
146)
A)
No
B)
Yes
Factor out the GCF.
147)
24wy2– 16w2y + 20wy
147)
A)
wy(24y – 16w + 20)
B)
4wy(6y – 4w + 20)
C)
4wy2(6 – 4w + 20wy)
D)
4wy(6y – 4w + 5)
21
Solve.
148)
4r – 7
2r
A cylindrical grain silo with a hemispherical top is shown above. Find an expression for the
volume of the silo and write the expression in factored form.
148)
A)
14
3r3– 7r2= 7r22
3r – 1
B)
14
3r3– 7r2= 2r27
3r – 1
C)
14
3r3– 7r2= 7r22
3r – 7
D)
14
3r3– 7r2= 7r32
3r – 1
Factor completely.
149)
t2–18t +80
149)
A)
(t –8)(t –10)
B)
(t –40)(t – 2)
C)
(t +8)(t +10)
D)
Prime
Factor the difference of cubes.
150)
8a3b6– 27b3
150)
A)
b3(2a – 3b)(4a2+ 6ab + 9b2)
B)
(2ab2– 3b)(4a2b4+ 6ab3+ 9b2)
C)
b3(2ab + 3)(4a2b2– 6ab + 9)
D)
b3(2ab – 3)(4a2b2+ 6ab + 9)
Factor the difference of squares.
151)
2x2–72y2
151)
A)
2(1 + 6xy)(1 – 6xy)
B)
2(x + 6y)(x – 6y)
C)
(2x + 6y)(2x – 6y)
D)
2(x – 6y)2
Factor by grouping.
152)
8sa +8sb –2a –2b
152)
A)
(a + b)(8s –2)
B)
(a – b)(8s +2)
C)
(a –2)(8s + b)
D)
(8a + b)(s–2)
Factor out the GCF.
153)
80x9y7– 48x3y4+ 80x5y2
153)
A)
16x3(5x6y7– 3y4+ 5x2y2)
B)
16x3y2(5x6y5– 3y2+ 5x2)
C)
16(5x9y7– 3x3y4+ 5x5y2)
D)
No common factor
Provide an appropriate response.
154)
Is x4y7 a common factor of –x5y8 and x4y7?
154)
A)
No
B)
Yes
22
155)
Is it possible to factor the expression 20x8(y + 7) + 9(y – 7)? If so, factor it.
155)
A)
Yes: (20x8+ 9 + 7 + y)
B)
Yes: (20x8+ 9)(y + 7)
C)
No
D)
Yes: (20x8+ 9)(y – 7)
Factor out the GCF.
156)
96m8n + 84m5n2+ 36m2n
156)
A)
m2n(96m6+ 84m3n + 36)
B)
12m8n2(8n + 7m3+ 3m6n)
C)
12m2n(8m6+ 7m3n + 3)
D)
12n(8m8+ 7m5n+ 3m2)
157)
7m(8– m) + 2n(8– m)
157)
A)
(7m – 2n)(8– m)
B)
m(7+ 2n)(8– 1)
C)
(7m + 2n)(8– m)
D)
No common factor
Solve.
158)
A science student watching a group of ants moving along a straight line determines that their
position x along the line as a function of time t is given by x(t) = t4 + 3t3 – 12t2 + 36t cm. Give an
equivalent expression for x(t) by factoring out a common factor.
158)
A)
t(t3+3t2+ 24t)
B)
t(t2+3t + 24)
C)
t(t2+3t – 24)
D)
t(t3+3t2–12t + 36)
Factor the difference of cubes.
159)
8p3–(m + n)3
159)
A)
(2p – m + n)(4p2+2pm +2pn +m2+ n)
B)
(2p – m – n)(4p2+2pm +2pn +m2+ 2mn +n2)
C)
(2p – m – n)(4p2+2pm –2pn +m2+ n)
D)
(2p + m + n)(4p2–2pm –2pn +m2+ 2mn +n2)
Factor by grouping.
160)
49x2– 56xy + 16y2
160)
A)
(49x+ 1)(x + 16)
B)
(7x – 4y)2
C)
(7x + 4y)2
D)
(7x – 4y)(7x + 4y)
Solve.
161)
n2=25
161)
A)
-5
B)
0, 5
C)
5
D)
-5, 5
162)
If an object is thrown upward with an initial velocity of 112 ft/sec, its height, h, in feet, after t
seconds is given by h = 112t – 16t2. Find the number of seconds before the object hits the ground.
(Round your answer to the nearest tenth, if necessary.)
162)
A)
3.5 sec
B)
7.5 sec
C)
7 sec
D)
56 sec
Factor the difference of squares.
163)
(8a – b)2–16
163)
A)
(8a –4b +4)(8a –4b –4)
B)
(8a + b +4)(8a – b –4)
C)
(8a – b +16)(8a – b –16)
D)
(8a – b +4)(8a – b –4)
23
Solve.
164)
3x4+32x3+64x2= 0
164)
A)
0, 8, 8
3
B)
–8, –8
3
C)
8, 8
3
D)
–8, –8
3, 0
165)
Given the expression 9x3+ 36x2 – 288x for the volume of a box, find the length, width, and height
of the box. Assume the length, width, and height are polynomial factors of the volume.
165)
A)
Length: x +8, width: x –4, height: 9x
B)
Length: x –8, width: x +4, height: 9x
C)
Length: 9x + 1, width: x –288, height: x
D)
Length: 9x +8, width: x –4, height: x
Factor by grouping.
166)
5m2+19mn +12n2
166)
A)
(m +3n)(5m +4n)
B)
(m –3n)(5m –4n)
C)
(m +3n)(4m +4n)
D)
(m +4n)(5m +3n)
Factor the difference of cubes.
167)
216–(p + q)3
167)
A)
(6 – p – q)(36 +6p +p2)
B)
(6 – p – q)(36 +6p +6q +p2+ 2pq +q2)
C)
(6 – p – q)3
D)
(6 + p + q)(36 –6p –6q +p2+ 2pq +q2)
Solve.
168)
A photo measuring 4 inches by 6 inches is mounted on a background measuring 6y inches by 9y
inches. Write an expression for the area of the border around the photo, then factor completely.
168)
A)
6(3y + 2)(3y– 2)
B)
6(3y- 2)2
C)
6(3y + 4)(3y– 4)
D)
(9y + 6)(6y– 4)
Use a graphing calculator to determine the x–intercepts.
169)
f(x) =4x2– 28x + 40
169)
A)
(0, 0), (2, 0), (5, 0)
B)
(4, 0), (2, 0), (5, 0)
C)
(2, 0), (5, 0)
D)
(–2, 0),(-5, 0)
Factor the difference of cubes.
170)
8a3– 27b3
170)
A)
(2a + 3b)(4a2– 6ab + 9b2)
B)
(8a – 3b)(a2+ 6ab + 9b2)
C)
(2a – 3b)(4a2+ 9b2)
D)
(2a – 3b)(4a2+ 6ab + 9b2)
Solve.
171)
The length of a rectangle is 8 inches more than its width. If 4 inches are taken from the length and
added to the width, the figure becomes a square with an area of 225 square inches. What are the
dimensions of the original figure?
171)
A)
15 in. by 15 in.
B)
15 in. by 19 in.
C)
11 in. by 19 in.
D)
11 in. by 15 in.
Factor by grouping.
172)
32r2+28ry –8xr –7xy
172)
A)
(7r +8y)(4r – x)
B)
(8r +7y)(4x – r)
C)
(8r +7y)(4r – x)
D)
(8r +7y)(x –4r)
24
Factor out the GCF.
173)
27m2n2– 24m3n + 27mn
173)
A)
3m(9mn2– 8m2n + 9n)
B)
3m2n(9n – 8m + 9)
C)
mn(27mn – 24m2+ 27)
D)
3mn(9mn – 8m2+ 9)
174)
2x5+2x
174)
A)
2x(x4+ 1)
B)
2x(x4)
C)
2(x6+ 1)
D)
2(x5+ x)
Factor the sum of cubes.
175)
8p3+m3n3
175)
A)
(2 + pmn)(4–2pmn +p2m2n2)
B)
(2p + mn)(4p2–2pmn +m2n2)
C)
(2p – mn)(4p2+2pmn +m2n2)
D)
(2p + mn)(4p2+m2n2)
Factor out the GCF.
176)
6(5 – 2b) + a(5– 2b)
176)
A)
(30 – 2b)(a – 2b)
B)
(5 + a)(6– 2b)
C)
(6 + a)(5– 2b)
D)
(6 + a)(30 – 2b)
Factor completely.
177)
64a6+b3a3
177)
A)
(4a2+ ba)(16a4–4ba3+b2a2)
B)
a3(4 + ab)(16 –4ab +b2a2)
C)
a3(4a – b)(16a2+4ab +b2)
D)
a3(4a + b)(16a2–4ab +b2)
Solve.
178)
Given the expression 49n2 – 9 for the area of a rectangle, find the length and width of the rectangle.
Assume the length and width are polynomial factors of the area.
178)
A)
Length: 7n +3, width: 7n –3
B)
Length: n +3, width: n –3
C)
Length: 7n +3, width: 7n +3
D)
Length: 49n +3, width: 49n –3
Find the GCF.
179)
48(a – b), 54(a – b)
179)
A)
6
B)
(a – b)
C)
6(a – b)
D)
48(a – b)
Solve.
180)
An automobile is traveling at 47 ft/sec. The driver applies the brakes in such a way that the velocity
decreases to zero according to the relation v(t) = 47 – 0.47t2, where t = time. Find an equivalent
expression for v(t) by factoring out a factor with a negative coefficient.
180)
A)
–47t(0.01t– 1)
B)
47(1 – 0.01t2)
C)
–47(0.01t2 – 1)
D)
–47(0.01t2 + 1)
Write a polynomial equation in standard form with the given solutions.
181)
–1
4, 9
181)
A)
4k2– 35k +9= 0
B)
9k2– 35k –4= 0
C)
k2– 35k – 9 = 0
D)
4k2– 35k – 9 = 0
25
Solve.
182)
16n2+ 28n = 0
182)
A)
0
B)
–7
4, 28
C)
–7
4
D)
–7
4, 0
Factor the sum of cubes.
183)
27 +(p – q)3
183)
A)
(3 – p + q)(9+3p –3q +p2– q)
B)
(3 – p + q)(9+3p –3q +p2– 2pq +q2)
C)
(3 + p – q)(9–3p +3q +p2– q)
D)
(3 + p – q)(9–3p +3q +p2– 2pq +q2)
Find the natural number b that makes the expression a perfect square trinomial.
184)
9x2– bx +64
184)
A)
1152
B)
24
C)
48
D)
576
Solve.
185)
Find the length of each side of the right triangle shown.
m4m – 6
3m + 6
185)
A)
14, 48, 50
B)
8, 26, 30
C)
15, 36, 39
D)
10, 36, 44
186)
A suitcase has a length of 9x inches, a width of 6x, and a height of 2x. A small box of height 2
inches, length 4 inches, and width 4 inches, is placed in the suitcase. The suitcase is otherwise
empty. Write an expression for the empty volume of the suitcase, then factor completely.
186)
A)
4(3x – 2)(9x2+ 12x + 4)
B)
4(3x – 2)(9x2+ 6x + 4)
C)
4(3x – 2)3
D)
4(3x + 2)(9x2– 6x + 4)
Factor by grouping.
187)
6–6s+s2–s3
187)
A)
(1 –s)(6+s2)
B)
(1 +s)(6–s2)
C)
(6 +s)(1 –s2)
D)
(6 –s)(1 +s2)
Factor out the GCF.
188)
28ab – 32a2– 40a
188)
A)
a(28b – 32a – 40)
B)
4a(7b – 8a – 10)
C)
4(7ab – 8a2– 10a)
D)
4a(7b – 32a2– 40a)
Factor completely.
189)
49ac +49cx –7ac2–7c2x
189)
A)
c(49 + c)(a –7x)
B)
7c(7– c)(a + x)
C)
7c(7– x)(a + c)
D)
7(7 –c2)(ac + x)
Solve.
190)
r(r –14) = –49
190)
A)
–7
B)
–7, 7
C)
7
D)
49, 7
26
191)
The area of a square is, numerically, 140 more than its perimeter. Find the length of a side.
191)
A)
56 units
B)
98 units
C)
392 units
D)
14 units
Factor completely.
192)
8x2–8x2y –56x +56xy
192)
A)
8(x – y)(x +7)
B)
8x(1 – y)(x –7)
C)
8x(y – 1)(x +7)
D)
x(1 – y)(8x –7)
Solve.
193)
A lamp shade has the geometric form as shown. The total surface area of a lamp shade with a slant
height s and top and bottom base radii of r2 and r1 is given by r12 + r22 + r1s + r2s. Find an
equivalent expression for the total surface area by factoring out a common factor.
193)
A)
(r12+r22+ sr1+ sr2)
B)
(r1+ r2)(r1+ r2+ s)
C)
(r1+ r2)(r1+ r2+ sr1r2)
D)
r1(r1+r22
r1+ s + sr2)
194)
m(m –12) +5(m –6) =-42
194)
A)
-3, 10
B)
6, 12
C)
-3, -4
D)
3, 4
195)
4x 4x
3x
9x
13x + 1
Find an expression for the area of the figure above and write the expression in factored form.
195)
A)
102x2+ 8x = 2x(51x + 4)
B)
102x2+ 6x = 6x(17x + 1)
C)
90x2+ 6x = 6x(15x + 1)
D)
102x2+ 6x = 6(17x2+ 6x)
Write a polynomial equation in standard form with the given solutions.
196)
9, -6
196)
A)
x2+9x -6 = 0
B)
x2– 3x – 54 = 0
C)
x2– 3x + 54 = 0
D)
x2+ 3x – 54 = 0
Find all natural–number values of b that make the trinomial factorable.
197)
x2–11x + b
197)
A)
10, 18, 24, 28
B)
10, 18, 24
C)
6, 7, 8, 9, 10
D)
10, 18, 24, 28, 30
27
Find the GCF.
198)
64a9b4, 88a5b9
198)
A)
8a9b9
B)
8a5b4
C)
704a9b9
D)
4a4b5
Solve.
199)
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the
length of the ladder if the length is 3 ft more than its distance from the wall.
199)
A)
12 ft
B)
15 ft
C)
18 ft
D)
9 ft
Factor out the GCF.
200)
–6x3–12x2+9x
200)
A)
–3x(2x2+ 4x – 3)
B)
–3(2x3+ 4x2– 3x)
C)
–3x(2x2– 4x + 3)
D)
–6x(x2+ 2x – 3)
Factor completely.
201)
8a2b2–8b3+20a2b –20b2
201)
A)
4b2(2b +5)(a2– 1)
B)
4b(2b + 1)(a2–5b)
C)
4b(2b +5)(a2– b)
D)
b(8b +1)(a2–20b)
Factor by grouping.
202)
6x3– 10x2y + 15xy2– 25y3
202)
A)
(3x + 5y)(2x2– 5y2)
B)
(3x – 5y)(2x2+ 5y2)
C)
(3x – 5y2)(2x2+ 5y)
D)
(6x + 5y)(x2– 5y2)
Factor completely.
203)
x3– x2– 20x
203)
A)
x(x + 4)(x – 5)
B)
(x2+ 1)(x – 20)
C)
x(x + 5)(x – 4)
D)
Prime
Solve.
204)
Throw Me for a Loop Bagels determines that it costs them C(x) = 60 + 1
2x – 1
80x2 dollars to make x
dozen bagels in one day. Find the equivalent expression for C(x) by factoring out 1
2.
204)
A)
1
2x(120 –1
40x)
B)
–1
2(120– x +1
40x2)
C)
1
2(120 + x –1
40x2)
D)
1
2(120 – x –1
40x2)
Factor the sum of cubes.
205)
2u3– 16
205)
A)
2(u – 2)(u2+ 2u +4)
B)
2(u + 2)(u2– 2u +4)
C)
(u + 2)(u2– 2u –4)
D)
(u – 2)(u2+ 2u +4)
28
Factor out the GCF.
206)
28wx – 12wy – 8w
206)
A)
4w(7x – 3y – 2)
B)
28w(x – 12y – 8)
C)
4w(7x – 3y – 8w)
D)
w(28x – 12y – 8)
Factor the difference of cubes.
207)
729– p3q3
207)
A)
(9p – q)(81p2+ 9pq +q2)
B)
(9 + pq)(81 –9pq +p2q2)
C)
(9 – pq)3
D)
(9 – pq)(81 + 9pq +p2q2)
Factor by grouping.
208)
5u2–24uv +27v2
208)
A)
(u –9v)(5u –3v)
B)
(u –3v)(5u –9v)
C)
(u +9v)(5u –3v)
D)
(u –3v)(5u +9v)
Factor the difference of cubes.
209)
64u3– 125u6v3
209)
A)
(4u + 5u2v)(16u2– 20u3v + 25u4v2)
B)
u3(4 + 5uv)(16 – 20uv + 25u2v2)
C)
(4u – 5u2v)(16u2+ 20u3v + 25u4v2)
D)
u3(4 – 5uv)(16 + 20uv + 25u2v2)
Factor by grouping.
210)
20p2q – 105pq2+ 100q3
210)
A)
5q(4p – 4q)(p – 5q)
B)
q(20p – 25q)(p – 4q)
C)
5(4p – 5q)(p – 4q2)
D)
5q(4p – 5q)(p – 4q)
Find the GCF.
211)
p2q4r, p5q2r3
211)
A)
p3q2r2
B)
p2q2
C)
p2q2r
D)
p3q2r3
Write a polynomial equation in standard form with the given solutions.
212)
-3, -2, 0
212)
A)
x3+5x2+6x = 0
B)
x3– 5x2– 6x = 0
C)
x3– 5x2+6x = 0
D)
x3+5x2– 6x = 0
Factor out the GCF.
213)
2(3 – x) – x(3– x)
213)
A)
(2 – x)(3– x)
B)
(3 –2x)(3– x)
C)
(2 – x)(3–x2)
D)
(6 – x)(3– x)
214)
9a6+36a3b
214)
A)
9a3(a3+ 4b)
B)
9a3b(a3+ 4)
C)
a3(9a3+36b)
D)
9(a6+ 4a3b)
Factor the trinomial containing two variables.
215)
u2– 2uv – 48v2
215)
A)
(u – 6v)(u + 8v)
B)
(u – v)(u + 8v)
C)
(u + 6v)(u – 8v)
D)
(u – 6v)(u + v)
29
Factor the difference of cubes.
216)
1000y3– 343
216)
A)
(10y – 7)3
B)
(10y – 7)(100y2+ 49)
C)
(10y – 7)(100y2+ 70y + 49)
D)
Prime
Factor out the GCF.
217)
3x2y6+24x2y5
217)
A)
y +8
B)
x2y5(3y +8)
C)
3x2y5(y +8)
D)
3x5y2(y +8)
Write a polynomial equation in standard form with the given solutions.
218)
0, 3, 7
218)
A)
x3+ 10x2+ 21x = 0
B)
x3+ 10x2– 21x = 0
C)
x3– 10x2+ 21x = 0
D)
x3– 10x2– 21x = 0
Factor the difference of squares.
219)
49x2– 81
219)
A)
(7x + 9)2
B)
(7x + 9)(7x – 9)
C)
(7x – 9)2
D)
Prime
Factor by grouping.
220)
m2s –m2t –ws +wt
220)
A)
(s – t)(m2+w)
B)
(s –m2)(t –w)
C)
(s – t)(m2–w)
D)
(s –w)(m2– t)
Factor completely.
221)
16a5–32a3b2+16ab4
221)
A)
a(16a2 – b2)2
B)
16a(a2–b2)(a2+b2)
C)
16a(a + b)2(a – b)2
D)
16(a2 – b2)2
222)
2m2n +6mn –4m2–12m
222)
A)
2m(m –3)(n +2)
B)
2(m2–3)(n +2m)
C)
2m(m +2)(n –3)
D)
2m(m +3)(n –2)
Solve.
223)
(x – 6)(x + 8) = 0
223)
A)
6, -8
B)
–6, 8
C)
6, 8
D)
6, -6, 8, -8
Factor by grouping.
224)
16p2–17pq +q2
224)
A)
(16p2– q)(1 – q)
B)
(17p – q)(p – q)
C)
(16p – q)(p – q)
D)
(16p + q)(p – q)
225)
10x2+ 15x – 6x – 9
225)
A)
(10x + 3)(x – 3)
B)
(10x – 3)(x + 3)
C)
(2x + 3)(5x – 3)
D)
(2x – 3)(5x + 3)
30
226)
15x2– 29xy + 12y2
226)
A)
(5x + 3y)(3x – 4y)
B)
(5x – 3y)(3x – 4y)
C)
(5x – 3)(3x – 4)
D)
(15x – 3y)(x – 4y)
Solve.
227)
4t3– 25t = 0
227)
A)
0
B)
–5
2, 5
2, 0
C)
5
2
D)
±5
2
Factor by grouping.
228)
y2+7ya +4y +28a
228)
A)
(y2+7a)(y+4)
B)
(y +7ya )(y+4)
C)
(y +7a)(y+4)
D)
(y +7)(y+4a)
Solve.
229)
(x + 3)(x – 6)(x – 17) = 0
229)
A)
-3, 6, -17
B)
-3, 6, 17
C)
0, -3, 6
D)
3, 6, 17
Factor the sum of cubes.
230)
512s3+216t3
230)
A)
(12s +6t)(64s2+36t2)
B)
(8s –6t)(64s2+48st +36t2)
C)
(8s +6t)(64s2+48st +36t2)
D)
(8s +6t)(64s2–48st +36t2)
Find the natural number b that makes the expression a perfect square trinomial.
231)
x2–16x + b
231)
A)
256
B)
16
C)
8
D)
64
Use the formula B = P 1 +r
nnt, which is used to calculate the final balance of an investment or a loan after being
compounded. Following is a list of what each variable represents:
B represents the final balance.
P represents the principal.
r represents the annual percentage rate.
t represents the time in years in which the principal is compounded.
n represents the number of times the principal is compounded in a year.
232)
Raul invests $40,000 in an account that is compounded annually. If, after two years, his balance is
$48,400, what was the interest rate of the account?
232)
A)
10%
B)
12%
C)
11%
D)
9%
Factor completely.
233)
6p2–6pq +p2q – pq2
233)
A)
p(p + q)(6– q)
B)
p(6p – q)(1 + q)
C)
p(p – q)(6+ q)
D)
(p2– q)(6+ pq)
Solve.
234)
n2–9= 0
234)
A)
-3
B)
3
C)
-3, 3
D)
0, 3
31
Factor completely.
235)
3x2+ 23x + 40
235)
A)
(3x + 1)(x + 40)
B)
(x – 35)(x + 5)
C)
(3x + 8)(x + 5)
D)
(x + 8)(3x + 5)
Factor the difference of cubes.
236)
8r3–27
236)
A)
(2r –9)(4r2–6r +3)
B)
(2r –3)(4r2+6r +9)
C)
(2r +3)(4r2–6r +9)
D)
(2r –3)(4r2–9)
Factor the sum of cubes.
237)
125+(y + 6)3
237)
A)
(y + 11)(y2–5y + 1)
B)
(y – 1)(y2+5y + 1)
C)
(–1– y)(y2+ 17y + 91)
D)
(y + 11)(y2+ 7y + 31)
Solve.
238)
x(x –6) =27
238)
A)
–3, 9
B)
–3, –9
C)
3, 9
D)
3, –9
Find the GCF.
239)
40u5v4w2, 24u6v5w, 32u3v6w5
239)
A)
24u6v6w5
B)
u3v4w
C)
8u6v6w5
D)
8u3v4w
Factor completely.
240)
a2b + 8ab – 20b
240)
A)
(a + 10b)(a – 2b)
B)
b(a + 10)(a – 2)
C)
b(a – 10)(a + 2)
D)
(a – 10b)(a + 2b)
Solve.
241)
The FDA approves a new drug and has confirmed by independent research that the strength of the
reaction to the drug is given by the formula S(d) = 1
2d2 – 1
3d3, where d is the dosage amount of
the drug and is a constant. Find an equivalent expression for S(d) by factoring out a common
factor.
241)
A)
d21
2+ 1
3d
B)
d21
2– 1
3d
C)
d2
31
2– d
D)
d2
2(– d)
Factor out the GCF.
242)
5x2+25x
242)
A)
5x2(x +5)
B)
x(5x +25)
C)
5x(x +25)
D)
5x(x +5)
Factor completely.
243)
a2(a + b)2– ab(a + b)2– 6b2(a + b)2
243)
A)
(a + b)2(a – 3)(a + 2)
B)
(a + b)2(a – 3b)(a + 2b)
C)
(a + b)2(a – 2b)(a + 3b)
D)
(a – 3b)(a + 2b)(a + b)
32
Factor the difference of squares.
244)
25k2– 4m2
244)
A)
(5k – 2m)2
B)
(5k + 2m)(5k – 2m)
C)
(5k + 2m)2
D)
Prime
Use a graphing calculator to solve the equation.
245)
18 + 3x =x2
245)
A)
6, 3
B)
-3, -6
C)
3, -6
D)
6, -3
Find the GCF.
246)
45x6y, 10x3y2
246)
A)
5x3y
B)
x3y
C)
10x6y
D)
5x6y2
Factor out the GCF.
247)
s(u + v) + t(u + v)
247)
A)
(s + u)(t + v)
B)
(s + t)(u + v)
C)
st(u + v)
D)
(s + t)(uv)
Factor the perfect square.
248)
16x2– 56x + 49
248)
A)
(4x – 7)(4x + 7)
B)
(4x – 7)2
C)
(4x + 7)2
D)
Prime
Solve.
249)
x2+ 4x – 96 = 0
249)
A)
–12, 8
B)
–12, 1
C)
12, 8
D)
12, -8
Factor the perfect square.
250)
16x2– 40xy + 25y2
250)
A)
(4x – 5y)2
B)
(16x+ 1)(x + 25)
C)
(4x + 5y)2
D)
(4x – 5y)(4x + 5y)
Factor completely.
251)
p2qr + 8pqr – 48qr
251)
A)
(pqr – 48)(p + qr)
B)
qr(p – 12)(p + 4)
C)
qr(p + 12)(p – 4)
D)
(pqr + 12)(p – 4qr)
Use a graphing calculator to solve the equation.
252)
2x2=-9x –9
252)
A)
3, – 3
2
B)
3, 3
2
C)
– 3
2, -3
D)
-3, -6
33
Solve.
253)
Sand is poured carefully into a pile that forms a right circular cone as shown. The total surface area
of a cone with slant height s and base radius r is the product of and the square of the radius
added to the product of , the radius, and the slant height. Write an expression for the total surface
area of the cone and then write the expression in factored form.
253)
A)
r2+rs =r(r + s)
B)
r2+r2s=r2(1 + s)
C)
r2+rs =r(r + s)
D)
r2+rs =rs(r + 1)
Use a graphing calculator to solve the equation.
254)
32 –x2=4x
254)
A)
4, -8
B)
-8, -4
C)
8, -4
D)
4, 8
Find the GCF.
255)
4x7y8, 16y2z4
255)
A)
4y2
B)
4xyz
C)
2y2
D)
x7y2
Factor out the GCF.
256)
xz – xy
256)
A)
x(z + y)
B)
xz(–xy)
C)
x
D)
x(z – y)
Factor the perfect square.
257)
b2–32b +256
257)
A)
(b + 16)2
B)
(b +16)(b –16)
C)
(b – 16)2
D)
Prime
Solve.
258)
x2– x –72 = 0
258)
A)
–8, -9
B)
1, 72
C)
8, 9
D)
–8, 9
34
259)
A rectangular space of 252 square feet is allocated for the living and dining areas in an apartment.
Find the width of the square living area given that the width of the dining area is 9 ft.
9 ft
Total Area: 252 sq. ft
259)
A)
11 ft
B)
12 ft
C)
14 ft
D)
21 ft
Use a graphing calculator to solve the equation.
260)
2x2+ 35 =x2+ 12x
260)
A)
5, 7
B)
6, -5
C)
35
2, 6
D)
35
2
Write a polynomial equation in standard form with the given solutions.
261)
5, 7
261)
A)
x2+12x – 35 = 0
B)
x2+12x + 35 = 0
C)
x2– 12x + 35 = 0
D)
x2–7x +5= 0
Find the natural number b that makes the expression a perfect square trinomial.
262)
9x2+ bx +25
262)
A)
450
B)
30
C)
15
D)
225
Use a graphing calculator to solve the equation.
263)
2x2+9=9x
263)
A)
-3, 3
2
B)
3
2, 3
C)
-3, – 3
2
D)
3, 6
Factor by grouping.
264)
4yx +3x +8y +6
264)
A)
(4y +3)(x +2)
B)
(4y +2)(x +3)
C)
(4y + 1)(x +6)
D)
(y +3)(4x +2)
265)
6wx –2wy –3xz + yz
265)
A)
(3x + y)(2w + z)
B)
(3x – z)(2w – y)
C)
(3x – y)(2w – z)
D)
(3wx – y)(2– z)
Find the GCF.
266)
104x3, 52x6
266)
A)
104x3
B)
26x3
C)
78x3
D)
52x3
35
Factor the difference of squares.
267)
p4– 81
267)
A)
(p2+ 9)(p+ 3)(p– 3)
B)
(p + 3)2(p – 3)2
C)
(p2+ 3)(p+ 3)(p– 3)
D)
(1 + 9p2)(1 – 9p2)
Factor the sum of cubes.
268)
512c3+ 343
268)
A)
(512c + 7)(c2– 56c + 49)
B)
(8c + 7)(64c2– 56c + 49)
C)
(8c – 7)(64c2+ 56c + 49)
D)
(8c + 7)(64c2+ 49)
Factor completely.
269)
2mn3–6mn +8mn2–24m
269)
A)
2(n2+3)(mn –4)
B)
2m(n2–3)(n +4)
C)
2(mn2–3)(n +4m)
D)
2m(n2+4)(n –3)
Solve.
270)
4x
3x
12x + 2
Find an expression for the area of the figure above and write an equivalent expression by factoring
out a common factor.
270)
A)
60x2+ 10x = 10x(6x + 1)
B)
60x2+ 10x = 60x(x + 1)
C)
60x2+ 10x = 10x2(6 + 10x)
D)
60x2+ 10x = 10x(6x + 10)
271)
Height
10 ft
Base
In the figure shown, the height of the triangular portion is 15 ft less than the base. The area of the
whole figure is 900 ft2. Find the base.
271)
A)
30 ft
B)
40 ft
C)
50 ft
D)
45 ft
Factor completely.
272)
3st2+ 3st– 36s
272)
A)
(3st + 9)(t – 4s)
B)
3s(t – 3)(t + 4)
C)
s(3t + 9)(t – 4)
D)
3s(t + 3)(t – 4)
Use a graphing calculator to determine the x–intercepts.
273)
f(x) = x2+ 5x – 14
273)
A)
(7, 0), (-2, 0)
B)
(–7, 0), (1, 0)
C)
(–7, 0), (2, 0)
D)
(7, 0), (2, 0)
36
Factor out the GCF.
274)
9s4t4+3s2t5
274)
A)
3s2t(3s + t)
B)
s2t4(9s +3t)
C)
3s2t4(3s2+ t)
D)
3s4t5(3s2+ t)
Factor completely.
275)
3uv3+3uv2–36uv
275)
A)
3v(uv +4)(uv –3)
B)
3uv(v –4)(v +3)
C)
uv(3v +36)(v –3)
D)
3uv(v +4)(v –3)
Factor out the GCF.
276)
m7–m5–m2
276)
A)
m2(m5–m3– m)
B)
m2(m5–m3– 1)
C)
m7(1 –m3–m5)
D)
No common factor
Solve.
277)
The product of two consecutive natural numbers is 29 more than their sum. Find the numbers.
277)
A)
6, 7 or -5, -4
B)
6, 7
C)
-5, -4
D)
5, 6
Provide an appropriate response.
278)
Is it possible to factor the expression 9x7(y + 7) + 7(y + 7)? If so, factor it.
278)
A)
No
B)
Yes: 9x7(y + 14)
C)
Yes: (y + 7)(9x7+ 7)
D)
Yes: 9x7(y + 7) + 7
Solve.
279)
5x2– 30x + 40 = 0
279)
A)
–2, -4
B)
5, 2, 4
C)
0, 2, 4
D)
2, 4
Factor completely.
280)
10z2+ 9z – 9
280)
A)
(10z + 3)(z – 3)
B)
(2z + 3)(5z – 3)
C)
(2z – 3)(5z + 3)
D)
(10z + 1)(z – 9)
Solve.
281)
The product of two consecutive integers is 6 less than 6 times their sum. Find the integers.
281)
A)
11, 12
B)
0, 1 or 11, 12
C)
0, 1
D)
0, 1 or 12, 13
Use a graphing calculator to verify that the factoring is correct. If it is not, write the correct factored form.
282)
49x3–14x2–42x =7x(x2–2x –6)
282)
A)
Correct form: 7x(7x2–2x –6)
B)
Correct form: x(49x2–14x –42)
C)
It is correct.
D)
Correct form: 7x(7x2–14x –42)
Factor out the GCF.
283)
x(y +8) – z(y +8)
283)
A)
(x + y)(–z +8)
B)
(x – z)(8y)
C)
(x – z)(y +8)
D)
xz(y +8)
37
Write a polynomial equation in standard form with the given solutions.
284)
-5, 0, 10
284)
A)
x3+ 5x2– 50x = 0
B)
x3+ 5x2+ 50x = 0
C)
x3– 5x2– 50x = 0
D)
x3– 5x2+ 50x = 0
Solve.
285)
Find three consecutive positive integers such that the sum of the squares of the smaller two is equal
to the square of the largest.
285)
A)
5, 6, 7
B)
3, 4, 5
C)
4, 5, 6
D)
–1, 0, 1
286)
A hemispherical bowl has a radius of 5 in. The volume of water in the bowl is found to be
5h2 – 1
3h3 cu. in. when it is h in. deep. Find an equivalent expression for the volume of water by
factoring out a common negative factor.
286)
A)
h21
3h – 5
B)
–h21
3h + 5
C)
–h21
3h – 5
D)
–h2(h –5)
287)
If the area of a square is given the expression 4x2 – 12x + 9, what is the length of each side?
287)
A)
2x +3
B)
2x –9
C)
2x –3
D)
4x –3
288)
The growth of revenue R(t) over a 12–year time period for Acme Computer Products is given by
R(t) = 0.7t + 28t2thousand dollars, where t = time in years. Find an equivalent expression for R(t)
by factoring out a common factor.
288)
A)
7t(0.1 +4t)
B)
4t(0.1 +7t)
C)
–7t(0.1 –4t)
D)
28(0.1t + t2)
Factor completely.
289)
10x2y2– 11xy2– 6y2
289)
A)
(5x – 3y)(2x + 2y)
B)
(2x – 3y)(5x + 2y)
C)
y2(2x – 3)(5x + 2)
D)
y2(x – 3)(10x + 2)
Factor using substitution.
290)
t4–50t2+625
290)
A)
t2(t – 25)2
B)
(t – 5)2(t + 5)2
C)
(t – 5)4
D)
(t2+25)(t –5)(t +5)
Factor out the GCF.
291)
6(b + 3c) – a(b + 3c)
291)
A)
(6 – a)(b + 3c)
B)
(b – a)(6+ 3c)
C)
(6b + 3c)(ab + 3c)
D)
(6b – ab)(b + 3c)
Factor by grouping.
292)
12xa –2xb +54ya –9yb
292)
A)
(6a – b)(2x +9y)
B)
(6a – y)(2x +9b)
C)
(6a +9y)(2x – b)
D)
(6a +9b)(2x – y)
Find the x–intercepts and then sketch the graph.
38
293)
f(x) = x3+ 2x2– 63x
293)
A)
(0, 0), (7, 0), (9, 0)
B)
(–9, 0), (0, 0), (7, 0)
C)
(–9, 0), (0, 0), (1, 0)
D)
(-7, 0), (0, 0), (9, 0)
Factor completely.
294)
15uv2+ 20uv – 75u
294)
A)
5u(3v + 3)(v – 5)
B)
5(3uv – 5)(v + 3)
C)
u(15v – 25)(v + 3)
D)
5u(3v – 5)(v + 3)
39
Solve.
295)
If an object is propelled upward from ground level with an initial velocity of 38.6 feet per second,
its height, h, in feet, t seconds later is given by the equation h = -16t2 + 38.6t. After how many
seconds does the object hit the ground? (Round your answer to the nearest tenth, if necessary.)
295)
A)
1.2 sec
B)
2.4 sec
C)
4.8 sec
D)
0.4 sec
296)
x3+ 4x2– 12x = 0
296)
A)
6, -2
B)
0, –6
C)
0, 2, 6
D)
–6, 0, 2
297)
x2+ 16x + 64 = 0
297)
A)
8
B)
–8, 8
C)
–8
D)
0, 8
298)
Acme Computer Products finds that the marginal revenue R in producing x computer networking
connectors is given by the polynomial function R(x) = 30 – 1
30x2 dollars/connector. Find an
equivalent expression for R(x) by factoring out 1
30x.
298)
A)
1
30x900
x + x
B)
1
30x(900– x)
C)
1
30x1
x – x
D)
1
30x900
x – x
Factor completely.
299)
(x –y)2–2(x –y) + 1
299)
A)
(x –y–1)(x–y)
B)
(x –y–1)(x–y+1)
C)
(x –y–1)2
D)
Prime
Solve.
300)
The height of a triangle is 5 cm more than the base. If the area of the triangle is 168 cm2, find the
height and the base.
300)
A)
Height: 22 cm; base: 15 cm
B)
Height: 21 cm; base: 16 cm
C)
Height: 16 cm; base: 11 cm
D)
Height: 20 cm; base: 15 cm
Factor the trinomial containing two variables.
301)
x2– 4xy + 4y2
301)
A)
(x – 2y)2
B)
(x – 2y)(x + 2y)
C)
(x + 2y)2
D)
Prime
Solve.
302)
(6x + 68)(x – 18) = (5x + 66)(x – 19)
302)
A)
18, 19
B)
–2, – 87
5, 3
4
C)
5, 6
D)
– 34
3, 18, – 66
5, 19
Factor by grouping.
303)
r2+3r +5r +15
303)
A)
(r –3)(r–5)
B)
(r +3)(r–5)
C)
(r +3)(r+5)
D)
r(r +15)
40
Factor the perfect square.
304)
m2+6m +9
304)
A)
(m – 3)2
B)
(m +3)(m –3)
C)
(m + 3)2
D)
Prime
Use a graphing calculator to determine the x–intercepts.
305)
f(x) = x3+ 4x2– 45x
305)
A)
(–9, 0), (0, 0), (5, 0)
B)
(–9, 0), (5, 0)
C)
(0, 0), (5, 0), (9, 0)
D)
(-5, 0), (0, 0), (9, 0)
Solve.
306)
x(2x + 10) = 0
306)
A)
0, –1
5
B)
0, 1
5
C)
0, 5
D)
0, -5
Factor out the GCF.
307)
r(s –4) +5(s –4)
307)
A)
r(s –4) +5
B)
(r +5)(s –4)
C)
(r –5)(s +4)
D)
5r(s –4)
Write a polynomial equation in standard form with the given solutions.
308)
2
3, –9
5
308)
A)
15x2+ 17x – 6
5= 0
B)
15x2+ 17x + 18 = 0
C)
15x2– 18x + 17 = 0
D)
15x2+ 17x – 18 = 0
Factor using substitution.
309)
x4– x2– 6
309)
A)
(x2+ 3)(x2– 2)
B)
(x2+ 2)(x2– 3)
C)
(x2+ 2)(x2+ 3)
D)
(x2+ 1)(x2– 6)
Solve.
310)
8x2=7x
310)
A)
8
7, 0
B)
– 7
8, 7
8
C)
7
8, 8
7
D)
7
8, 0
Use a graphing calculator to solve the equation.
311)
x2+ 13x =-36
311)
A)
4, 9
B)
-9, -4
C)
9, -4
D)
-9, 4
41
Answer Key
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Answer Key
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Answer Key
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Answer Key
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Answer Key
Testname: C6
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Answer Key
Testname: C6
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Answer Key
Testname: C6
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