1.
Find (3
a
- 1)(5
a
+ 6).
A.
15
a
2
+ 13
a
- 6
B.
15
a
2
- 5
a
- 6
C.
15
a
+ 13
a
-6
D.
15
a
2
+ 13
a
+ 6
Hint
2.
Factor 6
x
3
y
+ 15
x
2
y
2
- 3
x
4
y
.
A.
x
y
(6
x
2
+ 15
x
y
- 3
x
3
)
B.
3
x
y
(2
x
2
+ 5
x
y
-
x
3
)
C.
x
2
y
(6
x
+ 15
y
- 3
x
2
)
D.
3
x
2
y
(2
x
+ 5
y
-
x
2
)
Hint
3.
Find (4
x
2
+ 3
x
) + (7
x
2
– 5
x
– 6).
A.
9
x
– 6
B.
11
x
2
– 8
x
– 6
C.
11
x
2
– 2
x
– 6
D.
11
x
4
– 2
x
2
– 6
Hint
4.
Find the sum (4
xy
2
– 3
x
2
y
– 5
xy
– 6) + (-5
xy
2
– 2
xy
+ 3).
A.
-
xy
2
– 3
x
2
y
– 3
xy
– 3
B.
4
xy
2
– 8
x
2
y
– 7
xy
– 3
C.
4
xy
2
– 7
xy
– 3
D.
-
xy
2
– 3
x
2
y
– 7
xy
– 3
Hint
5.
Find (3
x
+ 4)(5
x
2
– 4
x
+ 6).
A.
15
x
3
+ 32
x
2
+ 34
x
+ 24
B.
15
x
3
+ 8
x
2
+ 2
x
+ 24
C.
5
x
2
+
x
+ 10
D.
8
x
2
- 13
x
+ 24
Hint
6.
Find the GCF of 54
a
2
, 84
ab
, and 10
c
A.
2
abc
B.
8
ab
C.
2
D.
4
Hint
7.
Factor 8
ac
+ 12
ad
+ 10
bc
+ 15
bd
.
A.
(8
ac
+ 12
ad
) + (10
bc
+ 15
bd
)
B.
(2
c
+ 3
d
) + (4
a
+ 5
b
)
C.
(2
c
+ 3
d
)(4
a
+ 5
b
)
D.
4
a
(2
c
+ 3
d
) + 5
b
(2
c
+ 3
d
)
Hint
8.
Factor 4
y
2
– 3
y
– 1.
A.
(4
y
– 1)(
y
+ 1)
B.
(2
y
+ 1)(2
y
– 1)
C.
(4
y
+ 1)(
y
– 1)
D.
prime
Hint
9.
Which of the following trinomials is a perfect square trinomial?
A.
9
a
2
- 12
a
+ 4
B.
4
y
2
+ 10
y
+ 25
C.
r
2
- 6
r
+ 36
D.
x
2
+ 16
x
+ 16
Hint
10.
Factor 4
x
2
– 49.
A.
B.
C.
(2
x
+ 7)(2
x
– 7)
D.
Hint
11.
A cafeteria has two meal plans. One requires the worker to pay $20 for the card, and $1 each time
x
she uses it. The other plan requires the worker to pay $30 for the card, but only $0.50 each time
x
she uses it. After how many uses will the workers with different plans have spent the same amount of money?
A.
It will never happen.
B.
20 uses
C.
10 uses
D.
5 uses
Hint
12.
Factor 4
x
2
– 14
x
– 8.
A.
2(2
x
+ 1)(
x
– 4)
B.
2(2
x
+ 1)(
x
– 2)
C.
(2
x
+ 1)(
x
– 2)
D.
(2
x
+ 1)(
x
– 4)
Hint
13.
Factor 81
x
2
– 225.
A.
9(3
x
– 5)(3
x
+ 5)
B.
It is prime.
C.
9(9
x
– 5)(9
x
+ 5)
D.
9(9
x
– 25)(9
x
+ 25)
Hint
14.
What is the area a triangle if
b
= 2
y
and
h
= 3
x
+ 5?
A.
6
xy
+ 10
y
B.
3
xy
+ 5
y
C.
D.
3
xy
+ 5
Hint
15.
Factor 5
xyz
- 5
xyw
- 5
xmz
+ 5
xmw
.
A.
(
z
-
w
)(5
xy
- 5
xm
)
B.
(5
z
-
w
)(
xy
+
xm
)
C.
(
z
-
w
)(
xy
-
xm
)
D.
(
z
+
w
)(5
xy
+ 5
xm
)
Hint
16.
Factor
x
2
- 2
x
- 8.
A.
(
x
- 2)(
x
+ 4)
B.
(
x
+ 8)(
x
+ 1)
C.
(
x
+ 2)(
x
- 4)
D.
(
x
- 8)(
x
+ 1)
Hint
17.
Factor
x
2
+
x
- 20.
A.
(
x
+ 2)(
x
+ 10)
B.
(
x
+ 5)(
x
- 4)
C.
(
x
+ 5)(
x
+ 4)
D.
(
x
- 5)(
x
+ 4)
Hint
18.
What is the coefficient of the second term in the polynomial expansion for (
a
+
b
)
4
?
A.
3
B.
5
C.
2
D.
4
Hint