1.
Find (3
a
- 1)(5
a
+ 6).
A.
15
a
2
+ 13
a
- 6
B.
15
a
2
+ 13
a
+ 6
C.
15
a
+ 13
a
-6
D.
15
a
2
- 5
a
- 6
Hint
2.
Find (
c
2
+ 2
c
- 6)(
c
+ 5).
A.
c
3
+ 2
c
2
+ 5
B.
c
3
+ 2
c
2
- 30
C.
c
3
+ 2
c
2
- 6
c
- 30
D.
c
3
+ 7
c
2
+ 4
c
- 30
Hint
3.
Factor 2
r
3
+ 8
r
2
- 10
r
completely.
A.
2(
r
3
+ 4
r
2
- 5
r
)
B.
2
r
(
r
2
+ 4
r
- 5)
C.
2
r
(
r
- 1)(
r
+ 5)
D.
(2
r
- 1)(
r
+ 5)
Hint
4.
Find the difference (-3
x
3
– 7
x
2
+ 5
x
– 4) – (6
x
2
– 8).
A.
-11
x
8
+ 4
B.
–3
x
3
– 13
x
2
+ 5
x
- 12
C.
–3
x
3
–
x
2
+ 5
x
- 12
D.
–3
x
3
– 13
x
2
+ 5
x
+ 4
Hint
5.
Find the GCF of 24, 36, and 108.
A.
12
B.
24
C.
6
D.
72
Hint
6.
Find the GCF of 54
a
2
, 84
ab
, and 10
c
A.
2
abc
B.
2
C.
8
ab
D.
4
Hint
7.
Factor 8
ac
+ 12
ad
+ 10
bc
+ 15
bd
.
A.
4
a
(2
c
+ 3
d
) + 5
b
(2
c
+ 3
d
)
B.
(2
c
+ 3
d
)(4
a
+ 5
b
)
C.
(2
c
+ 3
d
) + (4
a
+ 5
b
)
D.
(8
ac
+ 12
ad
) + (10
bc
+ 15
bd
)
Hint
8.
An expression for the area of a rectangle is
xy
– 2
x
+ 3
y
– 6. Express this area in factored form.
A.
(
xy
– 2
x
)( 3
y
– 6)
B.
(
x
+ 3)(
y
– 2)
C.
(
x
– 2)(
y
+ 3)
D.
x
(
y
– 2) + 3(
y
– 2)
Hint
9.
Factor 3
y
2
+ 7
y
+ 4.
A.
(3
y
+ 4)(
y
+ 1)
B.
(3
y
+ 1)(
y
+ 7)
C.
(3
y
+ 1)(
y
+ 4)
D.
(3
y
+ 2)(
y
+ 2)
Hint
10.
Which of the following trinomials is a perfect square trinomial?
A.
r
2
- 6
r
+ 36
B.
4
y
2
+ 10
y
+ 25
C.
x
2
+ 16
x
+ 16
D.
9
a
2
- 12
a
+ 4
Hint
11.
Factor
x
2
-
y
4
A.
(
x
+
y
2
)(
x
+
y
)(
x
–
y
)
B.
(
x
+
y
)(
x
–
y
)
C.
(
x
-
y
2
)(
x
+
y
2
)
D.
(
x
-
y
2
)(
x
-
y
2
)
Hint
12.
Determine whether the expression 5
x
3
y
3
–
x
2
y
2
is a polynomial.
A.
Cannot be determined from given information.
B.
No, because there are two terms.
C.
Yes.
D.
No, because there are two variables.
Hint
13.
Factor 4
x
2
– 49.
A.
(2
x
+ 7)(2
x
– 7)
B.
C.
D.
Hint
14.
Factor 5
x
2
+ 13
x
– 6.
A.
(5
x
+ 3)(
x
– 2)
B.
(5
x
– 2)(
x
+ 3)
C.
(5
x
+ 2)(
x
– 3)
D.
not factorable
Hint
15.
What is the area a triangle if
b
= 2
y
and
h
= 3
x
+ 5?
A.
3
xy
+ 5
y
B.
6
xy
+ 10
y
C.
3
xy
+ 5
D.
Hint
16.
Simplify
A.
B.
C.
D.
Hint
17.
Factor
x
2
- 7
x
+ 12.
A.
(
x
- 6)(
x
- 2)
B.
(
x
+ 6)(
x
+ 2)
C.
(
x
+ 3)(
x
+ 4)
D.
(
x
- 3)(
x
- 4)
Hint
18.
What is the coefficient of the fifth term in the polynomial expansion for (
a
+
b
)
5
?
A.
5
B.
6
C.
3
D.
10
Hint