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.
Find the GCF of 14
a
2
b
4
c
and 56
ab
2
c
2
A.
56
a
2
b
2
c
2
B.
14
ab
2
c
C.
56
ab
2
c
D.
14
a
2
b
4
c
2
Hint
3.
Factor
xy
– 6 + 2
y
– 3
x
.
A.
(
x
– 2)(
y
– 3)
B.
(
xy
– 3
x
) + (2
y
– 6)
C.
(
x
+ 2)(
y
– 3)
D.
x(y
– 3) + 2(
y
– 3)
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
(
y
– 2) + 3(
y
– 2)
B.
(
x
– 2)(
y
+ 3)
C.
(
x
+ 3)(
y
– 2)
D.
(
xy
– 2
x
)( 3
y
– 6)
Hint
5.
Factor
r
4
– 81.
A.
(
r
2
+ 9)(
r
+ 3)(
r
- 3)
B.
(
r
+ 3)
2
(
r
+ 3)
2
C.
prime
D.
(
r
2
+ 9)(
r
2
+ 9)
Hint
6.
Factor
A.
B.
C.
D.
prime
Hint
7.
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.
The sum of
b
and
c
is equal to the product of m and
n
.
C.
The product of
b
and
c
is equal to the sum of m and
n
.
D.
Their sum is equal to
c
, and their product is equal to
b
.
Hint
8.
Suppose the area of a square is
x
2
– 10
x
+ 25. What is the perimeter of the square?
A.
4
x
B.
2
x
C.
4
x
– 20
D.
2
x
– 10
Hint
9.
Factor 5
x
2
+ 13
x
– 6.
A.
(5
x
– 2)(
x
+ 3)
B.
(5
x
+ 3)(
x
– 2)
C.
not factorable
D.
(5
x
+ 2)(
x
– 3)
Hint
10.
Solve –3
x
2
+ 5
x
+ 12 = 0.
A.
B.
C.
D.
Hint
11.
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
12.
Solve the equation
x
2
–
x
+
= 0.
A.
B.
C.
D.
Hint