1.
Find the prime factorization of 324.
A.
2
2
· 3
3
B.
3
4
· 4
C.
2
2
· 3
2
· 9
D.
2
2
· 3
4
Hint
2.
Factor -180
x
2
y
2
A.
2
2
· 3
2
· 5 ·
x
·
x
·
y
·
y
B.
4 · 9 · 5 ·
x
·
x
·
y
·
y
C.
-1 · 2
2
· 3
2
· 5 ·
x
·
x
·
y
·
y
D.
-1 · 2
2
· 9 · 5 ·
x
·
x
·
y
·
y
Hint
3.
Factor 12
a
2
b
+ 30
ab
2
A.
ab
(12
a
+ 30
b
)
B.
6
ab
(2
a
+ 5
b
)
C.
6
ab
(6
a
+ 24
b
)
D.
6(2
a
2
b
+ 5
ab
2
)
Hint
4.
Factor 8
ac
+ 12
ad
+ 10
bc
+ 15
bd
.
A.
(2
c
+ 3
d
) + (4
a
+ 5
b
)
B.
(8
ac
+ 12
ad
) + (10
bc
+ 15
bd
)
C.
4
a
(2
c
+ 3
d
) + 5
b
(2
c
+ 3
d
)
D.
(2
c
+ 3
d
)(4
a
+ 5
b
)
Hint
5.
Factor 2
x
2
+ 4
x
– 3.
A.
prime
B.
(2
x
– 1)(
x
+ 3)
C.
(2
x
+ 3)(
x
– 1)
D.
(2
x
– 3)(
x
+ 1)
Hint
6.
Factor 7
xy
2
- 28
x
3
A.
(7
xy
+
x
)(
y
– 28
x
2
)
B.
7
x
2
y
2
(1 +
x
)
C.
prime
D.
7
x
(
y
+ 2
x
)(
y
- 2
x
)
Hint
7.
Factor 10
x
2
+ 24
x
+ 8.
A.
2(
x
+ 4)(5
x
+ 1)
B.
(
x
+ 2)(5
x
+ 2)
C.
2(
x
+ 2)(5
x
+ 2)
D.
(2
x
+ 4)(5
x
+ 2)
Hint
8.
Solve
a
2
– 12
a
= -27.
A.
a
= 3
B.
a
= -27 or
a
= -15
C.
a
= 9
D.
a
= 3 or
a
= 9
Hint
9.
When factoring quadratic trinomials of the form
x
2
+
b
x
+
c
, what is true about
m
and
n
if the factored form is (
x
+ m)(
x
+
n
)?
A.
Their sum is equal to
b
, and their product is equal to
c
.
B.
Their sum is equal to
c
, and their product is equal to
b
.
C.
The product of
b
and
c
is equal to the sum of m and
n
.
D.
The sum of
b
and
c
is equal to the product of m and
n
.
Hint
10.
Factor 4
x
2
– 14
x
– 8.
A.
2(2
x
+ 1)(
x
– 4)
B.
(2
x
+ 1)(
x
– 4)
C.
2(2
x
+ 1)(
x
– 2)
D.
(2
x
+ 1)(
x
– 2)
Hint
11.
Factor 16
b
4
– 36
b
2
.
A.
2
b
2
(4
b
– 3)(4
b
+ 3)
B.
4
b
2
(4
b
– 3)(4
b
+ 3)
C.
2
b
2
(2
b
– 3)(2
b
+ 3)
D.
4
b
2
(2
b
– 3)(2
b
+ 3)
Hint
12.
Solve the equation
x
2
–
x
+
= 0.
A.
B.
C.
D.
Hint