1.
Which of the following values is prime?
A.
72
B.
81
C.
53
D.
96
Hint
2.
Find the prime factorization of 324.
A.
2
2
· 3
3
B.
3
4
· 4
C.
2
2
· 3
4
D.
2
2
· 3
2
· 9
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.
(
x
2
+
y
2
)(3
x
+ 2
y
)
D.
xy
(3
x
2
+ 2
x
+ 3
y
+ 2
y
2
)
Hint
4.
An expression for the area of a rectangle is
xy
– 2
x
+ 3
y
– 6. Express this area in factored form.
A.
(
x
+ 3)(
y
– 2)
B.
x
(
y
– 2) + 3(
y
– 2)
C.
(
x
– 2)(
y
+ 3)
D.
(
xy
– 2
x
)( 3
y
– 6)
Hint
5.
Solve 3
x
2
+ 5 = 8
x
.
A.
or
x
= 1
B.
x
= 1
C.
x
= 0
D.
x
= 5 or
x
= 1
Hint
6.
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
7.
Factor
x
2
– 4
x
– 32.
A.
(
x
– 16)(
x
+ 2)
B.
(
x
– 8)(
x
+ 4)
C.
(
x
+ 8)(
x
– 4)
D.
(
x
+16)(
x
– 2)
Hint
8.
Factor 5
x
2
+ 13
x
– 6.
A.
(5
x
+ 3)(
x
– 2)
B.
(5
x
+ 2)(
x
– 3)
C.
not factorable
D.
(5
x
– 2)(
x
+ 3)
Hint
9.
Factor 3
x
3
+ 3
x
2
– 12
x
– 12.
A.
(
x
– 2)(
x
+ 2)(
x
+ 1)
B.
(
x
– 2)(
x
– 2)(
x
+ 1)
C.
3(
x
– 2)(
x
+ 2)(
x
+ 1)
D.
3(
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.
4 ft.
B.
2 ft.
C.
D.
Hint
11.
Factor 81
x
2
– 225.
A.
It is prime.
B.
9(3
x
– 5)(3
x
+ 5)
C.
9(9
x
– 5)(9
x
+ 5)
D.
9(9
x
– 25)(9
x
+ 25)
Hint
12.
Solve the following: (
q
+ 2)
2
= 25.
A.
{–7, 3}
B.
{3}
C.
{–7}
D.
{–3, 3}
Hint