1.
Select the correct factorization.
A.
66
ax
3
= 2 · 33 ·
a
·
x
·
x
B.
57
axy
2
= 57 ·
a
·
x
·
y
·
y
·
y
C.
–49
z
3
b
2
= –1 · 7 · 7 ·
z
·
z
·
b
·
b
D.
52
b
2
c
= 2 · 2 · 13 ·
b
·
b
·
c
Hint
2.
The product of the prime factors common to two integers is called the _____.
A.
least common denominator
B.
composite term
C.
greatest common factor
D.
prime factorization
Hint
3.
Factor the polynomial 33
x
2
– 3
xz
+ 45
xy
.
A.
3
x
(11
x
– z + 15
y
)
B.
3(11
x
2
–
xz
+ 15
xy
)
C.
3
x
(11
x
+ 15
y
)
D.
3
x
(11
x
– 1 + 15
y
)
Hint
4.
Factor the trinomial 4
x
3
– 24
x
2
– 108
x
.
A.
4(
x
– 9
x
)(
x
+ 3
x
)
B.
4
x
(
x
2
– 6
x
– 27)
C.
(
x
– 9)(
x
+ 3)
D.
4
x
(
x
– 9)(
x
+ 3)
Hint
5.
Factor the trinomial 10
x
2
+ 13
x
– 3.
A.
prime
B.
(2
x
– 3)(5
x
+ 1)
C.
(2
x
– 1)(5
x
+ 3)
D.
(2
x
+ 3)(5
x
– 1)
Hint
6.
The measure of the volume of a rectangular prism is 12
x
3
+ 22
x
2
– 20
x
. What are possible dimensions of the prism?
A.
2
x
, 6
x
+ 2,
x
– 5
B.
2
x
, 2
x
+ 5, 3
x
– 2
C.
2
x
, 2
x
– 5, 3
x
+ 2
D.
2
x
,
x
+ 5, 6
x
– 2
Hint
7.
Factor the trinomial 9
b
2
– 24
b
+ 16.
A.
(3
b
– 4)(3
b
+ 4)
B.
(3
b
+ 2)(3
b
– 8)
C.
(3
b
– 4)
2
D.
prime
Hint
8.
Divide 36
jk
3
– 42
j
3
k
by 6
jk
.
A.
7
k
– 6
j
2
B.
6jk – 7
j
2
k
C.
7jk – 6
j
2
k
D.
6
k
2
– 7
j
2
Hint
9.
Factor 3
x
2
– 10
x
y
– 8
y
2
.
A.
(
x
– 2
y
)(3
x
– 4
y
)
B.
(3
x
+ 2
y
)(
x
– 4
y
)
C.
(
x
+ 2
y
)(3
x
– 4
y
)
D.
(3
x
– 2
y
)(
x
– 4
y
)
Hint
10.
Which of these represents factoring differences of squares?
A.
a
2
–
b
2
= (
a
–
b
)(
a
+
b
)
B.
a
2
– 2
a
b
+
b
2
= (
a
–
b
)(
a
–
b
)
C.
a
2
+ 2
a
b
+
b
2
= (
a
+
b
)(
a
+
b
)
D.
a
2
+
b
2
= (
a
–
b
)(
a
+
b
)
Hint