1.
Factor 54
x
3
y
2
A.
2 · 3
3
·
x
·
x
·
y
·
y
·
y
B.
2 · 27 ·
x
·
x
·
x
·
y
·
y
C.
2
3
· 3 ·
x
·
x
·
x
·
y
·
y
D.
2 · 3
3
·
x
·
x
·
x
·
y
·
y
Hint
2.
Factor
xy
– 6 + 2
y
– 3
x
.
A.
(
xy
– 3
x
) + (2
y
– 6)
B.
x(y
– 3) + 2(
y
– 3)
C.
(
x
– 2)(
y
– 3)
D.
(
x
+ 2)(
y
– 3)
Hint
3.
Factor 3
y
2
+ 7
y
+ 4.
A.
(3
y
+ 4)(
y
+ 1)
B.
(3
y
+ 2)(
y
+ 2)
C.
(3
y
+ 1)(
y
+ 7)
D.
(3
y
+ 1)(
y
+ 4)
Hint
4.
Factor 4
y
2
– 9.
A.
(2
y
+ 3)(2
y
+ 3)
B.
prime
C.
(2
y
+ 3)(2
y
– 3)
D.
(2
y
– 3)(2
y
– 3)
Hint
5.
Solve
x
2
–
x
– 72 = 0.
A.
x
= -8
B.
x
= 8 or
x
= -9
C.
x
= -8 or
x
= 9
D.
x
= 9
Hint
6.
Is 79 prime or composite? If it is composite, what is its factorization?
A.
composite, 7 × 11
B.
composite, 13 × 6
C.
composite, 3 × 23
D.
prime
Hint
7.
If the product of two factors is 0, which of the following cannot be true?
A.
One of the factors is 10.
B.
Both of the factors are 0.
C.
One of the factors is 0.
D.
Neither of the factors is 0.
Hint
8.
Factor
x
2
– 4
x
– 32.
A.
(
x
– 16)(
x
+ 2)
B.
(
x
– 8)(
x
+ 4)
C.
(
x
+16)(
x
– 2)
D.
(
x
+ 8)(
x
– 4)
Hint
9.
Factor 3
x
2
– 8
x
+ 3.
A.
not factorable
B.
(
x
– 1)(3
x
– 3)
C.
(3
x
– 5)(
x
– 1)
D.
(3
x
– 1)(
x
– 3)
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.
2 ft.
B.
C.
4 ft.
D.
Hint
11.
Factor 81
x
2
– 225.
A.
It is prime.
B.
9(9
x
– 5)(9
x
+ 5)
C.
9(3
x
– 5)(3
x
+ 5)
D.
9(9
x
– 25)(9
x
+ 25)
Hint
12.
Solve the following:
y
2
+ 6
y
+ 9 = 49.
A.
{–10, 4}
B.
{10, –4}
C.
{7, –7}
D.
{7}
Hint