1.
Find the prime factorization of 324.
A.
2
2
· 3
2
· 9
B.
2
2
· 3
4
C.
3
4
· 4
D.
2
2
· 3
3
Hint
2.
Factor -180
x
2
y
2
A.
4 · 9 · 5 ·
x
·
x
·
y
·
y
B.
-1 · 2
2
· 3
2
· 5 ·
x
·
x
·
y
·
y
C.
2
2
· 3
2
· 5 ·
x
·
x
·
y
·
y
D.
-1 · 2
2
· 9 · 5 ·
x
·
x
·
y
·
y
Hint
3.
Factor 12
a
2
b
+ 30
ab
2
A.
6(2
a
2
b
+ 5
ab
2
)
B.
6
ab
(2
a
+ 5
b
)
C.
6
ab
(6
a
+ 24
b
)
D.
ab
(12
a
+ 30
b
)
Hint
4.
Factor
xy
– 6 + 2
y
– 3
x
.
A.
(
x
– 2)(
y
– 3)
B.
(
x
+ 2)(
y
– 3)
C.
x(y
– 3) + 2(
y
– 3)
D.
(
xy
– 3
x
) + (2
y
– 6)
Hint
5.
Factor 2
x
2
+ 4
x
– 3.
A.
prime
B.
(2
x
– 3)(
x
+ 1)
C.
(2
x
– 1)(
x
+ 3)
D.
(2
x
+ 3)(
x
– 1)
Hint
6.
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.
The product of
b
and
c
is equal to the sum of m and
n
.
B.
Their sum is equal to
b
, and their product is equal to
c
.
C.
The sum of
b
and
c
is equal to the product of m and
n
.
D.
Their sum is equal to
c
, and their product is equal to
b
.
Hint
7.
Suppose the area of a square is
x
2
– 10
x
+ 25. What is the perimeter of the square?
A.
2
x
B.
2
x
– 10
C.
4
x
– 20
D.
4
x
Hint
8.
Factor 4
x
2
– 14
x
– 8.
A.
2(2
x
+ 1)(
x
– 4)
B.
(2
x
+ 1)(
x
– 4)
C.
2(2
x
+ 1)(
x
– 2)
D.
(2
x
+ 1)(
x
– 2)
Hint
9.
Factor 3
x
3
+ 3
x
2
– 12
x
– 12.
A.
(
x
– 2)(
x
– 2)(
x
+ 1)
B.
3(
x
– 2)(
x
– 2)(
x
+ 1)
C.
3(
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.
B.
C.
4 ft.
D.
2 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