1.
Find the GCF of 54
a
2
, 84
ab
, and 10
c
A.
4
B.
2
C.
8
ab
D.
2
abc
Hint
2.
Factor 12
a
2
b
+ 30
ab
2
A.
6(2
a
2
b
+ 5
ab
2
)
B.
6
ab
(6
a
+ 24
b
)
C.
6
ab
(2
a
+ 5
b
)
D.
ab
(12
a
+ 30
b
)
Hint
3.
Factor 3
x
3
+ 2
x
2
y
+ 3
xy
2
+ 2
y
3
A.
(3
x
+ 2
y
)(
x
+
y
)(
x
-
y
)
B.
x
2
(3
x
+ 2
y
) +
y
2
(3
x
+ 2
y
)
C.
xy
(3
x
2
+ 2
x
+ 3
y
+ 2
y
2
)
D.
(
x
2
+
y
2
)(3
x
+ 2
y
)
Hint
4.
Factor
x
2
+ 5
x
+ 6.
A.
(
x
+ 1)(
x
+ 6)
B.
(
x
+ 2)(
x
+ 3)
C.
(
x
+ 1)(
x
+ 5)
D.
prime
Hint
5.
Factor 3
y
2
+ 7
y
+ 4.
A.
(3
y
+ 1)(
y
+ 7)
B.
(3
y
+ 4)(
y
+ 1)
C.
(3
y
+ 2)(
y
+ 2)
D.
(3
y
+ 1)(
y
+ 4)
Hint
6.
Solve 3
x
2
+ 5 = 8
x
.
A.
x
= 5 or
x
= 1
B.
x
= 1
C.
or
x
= 1
D.
x
= 0
Hint
7.
Find the prime factorization of -198.
A.
2 · 3
2
· 11
B.
–1 · 2 · 3
2
· 10
C.
2 · 3
2
· 10
D.
–1 · 2 · 3
2
· 11
Hint
8.
Factor
x
2
+ 6
x
– 7.
A.
(
x
+ 1)(
x
– 7)
B.
(
x
+ 3)(
x
+ 3)
C.
(
x
– 1)(
x
+ 7)
D.
(
x
– 3)(
x
– 3)
Hint
9.
Factor 3
x
3
+ 3
x
2
– 12
x
– 12.
A.
3(
x
– 2)(
x
– 2)(
x
+ 1)
B.
3(
x
– 2)(
x
+ 2)(
x
+ 1)
C.
(
x
– 2)(
x
+ 2)(
x
+ 1)
D.
(
x
– 2)(
x
– 2)(
x
+ 1)
Hint
10.
Suppose that we have a 3 ft. × 3 ft. piece of paper, and we cut out a square piece so that the area of the remaining piece is 5 feet. What is the length of a side of the square?
A.
2 ft.
B.
C.
D.
4 ft.
Hint
11.
Determine whether the trinomial 9
x
2
– 60
x
+ 25 is a perfect square trinomial. If so, factor it.
A.
(3
x
+ 5)(3
x
+ 5)
B.
(3
x
– 5)(3
x
+ 5)
C.
It is prime.
D.
(3
x
– 5)(3
x
– 5)
Hint
12.
Solve the equation
x
2
–
x
+
= 0.
A.
B.
C.
D.
Hint