Free Printable Factoring and exponents

1.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

2.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

3.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

4.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

5.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

6.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

7.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

8.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

9.

a)

b)

c)

d)

10.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

11.

a)

b)

c)

d)

12.

a)

b)

c)

d)

13.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

14.

Write with positive exponents:

1/a^-2

a)

a^-2

b)

a²

c)

1/a¹

15.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

16.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

17.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

18.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

19.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

20.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

21.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

22.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

23.

According to exponent rules, when we divide powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

31.

a)

b)

c)

d)

32.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

33.

(8⁵)³

a)

8⁸

b)

8¹⁵

c)

8²

d)

1/8²

34.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

35.

Simplify $\left(y^8\right)^9$

a)

$y^{72}$

b)

$9y^{72}$

c)

$9y^8$

d)

$y^{17}$

36.

Simplify $\left(5^3\right)^{10}$

a)

$25^3$

b)

$5^{13}$

c)

$25^{30}$

d)

$5^{30}$

37.

Simplify $\left(-7^2\right)^7$

a)

$\left(-49\right)^{14}$

b)

$\left(-7\right)^9$

c)

$\left(-7\right)^{14}$

d)

$\left(-49\right)^2$

38.

Simplify: $\ \left(y^3\right)^{-2}$

(Choose two answers)

a)

$y^5$

b)

$y^{-6}$

c)

$\frac{1}{y^6}$

d)

$\frac{y^3}{y^2}$

39.

$365^0=$

a)

0

b)

1

c)

365

d)

$\frac{1}{365}$

40.

According to exponent rules, when we multiply two powers with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

41.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

42.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

43.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

44.

$x^2y^0=$ Hint: the zero exponent is only applied to the letter y.

a)

1

b)

$x^2$

c)

0

d)

z

45.

x³⋅x² =

a)

x⁵

b)

x⁶

c)

x⁹

d)

x¹

46.

a)

b)

c)

d)

47.

Evaluate this expression using the quotient of powers rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

48.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

49.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

50.

n⋅n⁴⋅n⁵

a)

n¹⁰

b)

n⁴⁰

c)

n¹³

d)

n²²

51.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

52.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

53.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

54.

Factor:

2n²-8n³

a)

2n²(n-4n²)

b)

-2n²(4n²-1)

c)

2n³(10-8n²)

d)

3n(1-4n)

55.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁶)

d)

3x²(80x³-40-60x⁵)

56.

Factor:
2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

57.

Factor:
10a⁴+16a+10a²

a)

2a(5a³⁺8+5a)

b)

2a⁴(5a+8a²+5a³)

c)

2a⁴(10+16a+40a²)

d)

3a³(5+8a+a²)

58.

Factor
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

59.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

60.

Find the prime factorization of 120.

a)

3 x 5 x 8

b)

2³ x 3 x 5

c)

2² x 3 x 5

d)

2 x 3² x 5

61.

Find the GCF of 64 and 144

a)

8

b)

6

c)

16

d)

2

62.

What is the GCF of 18k and 15k³

a)

3k²

b)

3k³

c)

3k

d)

5k

63.

What is the GCF of 10a²b³ and 20a²b²?

a)

20a²b³

b)

10a²b³

c)

20ab²

d)

10a²b²

64.

39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

65.

63x⁴ - 7x² + 28x

a)

7x(9x² - 7 + 4x)

b)

x(63x³ - 7x + 28)

c)

7x(9x³ - x + 4)

66.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

67.

Factor
18a²b⁴c + 24ab³c²

a)

6ab³c(3ab + 4c)

b)

3abc(6ab³+ 8b²c)

c)

6abc(3ab³ + 4c)

d)

6ab3c(3b + 4c)

68.

Factor
18a²b⁴c + 24ab³c²

a)

6ab³c(3ab + 4c)

b)

3abc(6ab³+ 8b²c)

c)

6abc(3ab³ + 4c)

d)

6ab3c(3b + 4c)

69.

What is the greatest common factor of the two terms in the expression x⁵y²+x²y⁷z

a)

x²

b)

x²y²z

c)

x²y²

d)

x⁵y⁷z

70.

Factor
5ab²c¹¹ + 2bc⁵

a)

bc⁵(5ab²c⁶ + 2b)

b)

bc⁵(5abc⁶ + 2)

c)

b²c⁵(5bc⁶ + 2)

d)

c4(5a²b²c⁷+ 2bc)

71.

Factor
-10xy⁹z + 8y³z⁵

a)

2y⁴z(-20xy⁶ + 4z⁴)

b)

2y³z(-5xy⁶ +4z⁴)

c)

2y³z(-5xy⁶z + 4z⁵)

d)

2y³z(-5xy⁶z + 8z⁴)

72.

Factor
12j²k³ - 20hj

a)

4j(3jk³ - 5h)

b)

4j(6jk³ - 10h)

c)

4j(3jk² - 5h)

d)

4j²(24j²k³ - 20h)

73.

Factor
20p²q² - 25pm

a)

pm(4q - 5m)

b)

5(4pq³ - 5m)

c)

pq(20pq² - 25m)

d)

5p(4pq² - 5m)

74.

what is the greatest common factor of the three terms in the expression
-24m³n⁵p + 24mn⁴p² + 4mn⁵

a)

4mn

b)

24mn⁴

c)

4mn⁴

d)

4mn⁴p

75.

Factor
49m³q² - 35mq² - 42m³q⁴p²

a)

7mq²(7m²q - 5 - 6m²p²q²)

b)

7mq²(7m³q - 5mq - 6m²p²q³)

c)

7mq²(7m² - 5 - 6m²p²q²)

d)

7mq²(7mq - 5 - 6m²pq²)

76.

Factor
8p³q⁴ - 3pq³m² + 6p³q²

a)

pq²(8p²q³ - 3m²q² + 6p²q)

b)

pq(32p²q² - 3m²q + 6p²)

c)

4q²(8p²q² - 3m²q + 6p²)

d)

pq²(8p²q² - 3m²q + 6p²)

77.

Factor
-8x²y² + 32yz + 40y

a)

8z(-x² + 4z +1)

b)

8y(-4x²y² + 16yz + 20y)

c)

8y(-x²y + 4z + 5)

d)

4y (-2x²y + 40z + 10)

78.

Factor
-64a⁴b - 96ab³ + 8a

a)

8a(-8a³b - 12b³ + a)

b)

8ab(-8a³ + 12b² + 1)

c)

8a(8a³b - 12b² + 1)

d)

8a(-8a³b - 12b³ + 1)

79.

What is the greatest common factor in the three terms -96xy - 144x - 84

a)

12

b)

-12

c)

12x

d)

-12x

80.

What is the greatest common factor of the three terms in the expression
-96xy - 144x - 84

a)

12x

b)

-12

c)

-12xy

d)

12

81.

Undistribute the following polynomial
10x + 10x² + 10x³ + 10x⁴ + 10x⁵

a)

x(10x + 10x² + 10x³ + 10x⁴)

b)

10(x² + x³ + x⁴ + x⁵)

c)

10x(1 + x + x² + x³ + x⁴)

d)

10x(x + x² + x³ + x⁴ + x⁵)

82.

Undistribute the following polynomial
5(c + 2)⁶ - 10(c + 2)⁴

a)

5(c + 2)⁴((c+2)² - 2)

b)

(c+2)⁴(5(c+2)² - 10)

c)

5(c+2)⁶ - 2(c+2)⁴

d)

5(c+2)⁴

83.

What is the greatest common factor of the following polynomial:
11(x - 3) + 22(x - 3)² + 55(x - 3)⁵+ 66(x - 3)⁴

a)

(x - 3)

b)

11

c)

11(x - 3)⁴

d)

11(x - 3)

84.

Factor
-84x⁴ + 72xy² + 12xy

a)

12x(-7x³ + 6y² + y)

b)

6x(-7x³ + 2y² + 1)

c)

4x(-7x³ + 6y² +y)

d)

12x(-7x² + 6y² + 1)

85.

What is the greatest common factor of the following polynomial:
-9xy - 81xy - 18 - 45xy

a)

9xy

b)

-9

c)

9x

d)

xy

86.

Factor
25a⁴b⁴ + 25a³b³ + 25a²b²

a)

25a⁴b⁴(ab + a²b² + 25)

b)

a²b²(25a²b² + 25ab + 25)

c)

25a²b²(a²b² + ab + 1)

d)

25a²b²(a²b² + ab + ab)

87.

Factor
500x³y³ + 1000x²y² + 1500xy

a)

500xy(x²y² + 2xy + 3)

b)

1500x³y³(3 + 2xy + xy)

c)

500xy(x²y² +500xy + 1000)

d)

500xy(x³y³ + x²y² + xy)

88.

Which expression is equivalent to

the polynomial: k²+7x+10?

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

89.

Which expression shows the factors of: n² + 16n + 63?

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

90.

Which expression is a factor of: k² -2k - 24

a)

(k-6)

b)

((k+2)

c)

(k-1)

d)

(k-5)

91.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

92.

Which expression shows the

factors of: x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

93.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

94.

The trinomial 4x²-20x + 25 is factorable.

Which of these is the correct factorization?

a)

(2x+5)(2x-5)

b)

$\left(2x-5\right)^2$

c)

$\left(2x+5\right)^2$

d)

$\left(x-5\right)\left(4x-5\right)$

95.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

96.

Which function is equivalent to: h(x)= 3x² + 10x - 8?

a)

h(x)=(3x + 2)(x + 4)

b)

h(x)=(7x + 5)(x + 2)

c)

h(x)=(3x - 2)(x + 4)

d)

h(x)=(7x - 3)(x - 4)

97.

The area of a rectangle painting is (x²+ 9x - 36) square units.

Which of the following could be the dimensions of the painting?

a)

(x + 12)units

by (x - 3) units.

b)

(x + 9) units

by (x - 4)units

c)

(x - 12) units

by (x + 3) units

d)

(x - 9)units

by (x - 4)units

98.

What are the factors of: x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

99.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

100.

Which factorization below is the complete factorization of the trinomial: $5x^2+10x-15?$

a)

5(x - 3)(x +1)

b)

5x(x+3)(x-1)

c)

5(x + 3)(x - 1)

d)

5x(x- 3)(x+1)

101.

What is the complete factorization of 3x²-3x - 18?

a)

3(x -2)(x - 3)

b)

3(x +3)(x -2)

c)

3x(x -3-6)

d)

3(x + 2)(x - 3)

102.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

103.

A box in the shape of a rectangular prism

is represented by the polynomial a² - a - 12,

where a is measured in centimeters.

Which measure might represent the box?

a)

(a - 4)cm and

(a + 3)cm.

b)

(a + 6)cm and

(a - 4)cm

c)

(a - 6)cm and

(a + 4) cm

d)

(a + 4) cm and

(a - 3)cm

104.

$x^2-x-20$

Which of the following is the complete factorization?

a)

(x-2)(x-10)

b)

(x-1)(x+20)

c)

(x+5)(x+4)

d)

(x-5)(x+4)

105.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

106.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

107.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

108.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

109.

2x³-8x²-x+4

a)

(2x²-1)(x-4)

b)

2(x²-1)(x+4)

c)

(x²-1)(2x-4)

d)

(2x²+1)(x-4)

110.

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

111.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

112.

x²+10x+16

a)

(x+2)(x+8)

b)

(x-2)(x-8)

c)

(x+1)(x+16)

d)

(x+6)(x+10)

113.

x²-17x+72

a)

(x+2)(x-36)

b)

(x-8)(x+9)

c)

(x-8)(x-9)

d)

(x-4)(x-7)

114.

5x²-15x+10

a)

(5x-2)(x-5)

b)

5(x-2)(x+1)

c)

Your Face

d)

5(x-2)(x-1)

115.

My name's Blurry Face and I ____________

a)

care what you think

b)

hate factoring

c)

need some better soap

d)

wash my clothes in the sink

116.

5x²+7x-24

a)

5(x-8)(x-3)

b)

(5x+12)(x-2)

c)

(x-8)(5x+3)

d)

(5x-8)(x+3)

117.

5x²-27x+10

a)

(5x-2)(x-5)

b)

(5x+2)(x+5)

c)

(5x+2)(x-5)

d)

5(x+2)(x-5)

118.

Don't get to close, it's dark inside. It's ____________________

a)

where my bicycles ride

b)

where my demons hide

c)

where I surf the tide

d)

Mr. Miller's forehead's wide

119.

7x²+12x+9

a)

(7x-3)(x-3)

b)

(7x+3)(x+3)

c)

(7x+1)(x+9)

d)

(7x+9)(x+1)

120.

28x²-120x+32

a)

4(7x-2)(x-4)

b)

(4x-2)(7x-4)

c)

7(x-2)(4x-4)

d)

(7x-2)(4x-16)

121.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

122.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

123.

2x³-8x²-x+4

a)

(2x²-1)(x-4)

b)

2(x²-1)(x+4)

c)

(x²-1)(2x-4)

d)

(2x²+1)(x-4)

124.

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

125.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

126.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

127.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

128.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

129.

Simplify the product. Write the answer in standard form.
(x+2)(x-5)

a)

x²-3x-10

b)

2x²-3

c)

x²-10

d)

x²+2x-10

130.

Simplify. Write your answer in standard form:
(3x³+9x²-2x)−(7x³-6x²+1)

a)

10x³+15x²-3x

b)

-4x³+3x²-2x+1

c)

-4x³+15x²-2x-1

d)

-4x³+15x²-2x+1

131.

7r³- 8r²+ 42r - 48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

132.

20x³- 25x²+ 4x - 5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

133.

Factor by grouping:

x³ + 7x² - 2x - 14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

134.

Factor by grouping:

4p³ + 8p² + 3p + 6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

135.

x²+ 8x + 2x + 16

a)

(x+2)(x+8)

b)

(x-2)(x-8)

c)

(x+1)(x+16)

d)

(x+6)(x+10)

136.

Factor

x²+ 12x - 3x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

137.

Factor

3a² + a + 3a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

138.

Factor completely.

2n² + 10n + 3n + 15

a)

(5n - 9)(n - 3)

b)

(3n + 7)(n + 4)

c)

(2n + 3)(n + 5)

d)

Not factorable

139.

Factor

9x² - 12x + 6x - 8

a)

(3x+2)(3x-4)

b)

(3x+2)(3x+4)

c)

(3x-2)(3x-4)

d)

(x-1)(9x+8)

140.

Factor

3v² + 3v - 7v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

141.

Factor:

6x² + 2x – 21x – 7

a)

(2x +7)(3x – 1)

b)

(1x – 1)(6x+7)

c)

(2x – 7)(3x+1)

d)

(6x – 7)(1x+1)

142.

Factor: 6x² + 21x + 4x + 14

a)

(3x - 2)(2x - 7)

b)

4(2x + 5)(3x - 4)

c)

(3x + 2)(2x + 7)

d)

6(x + 2)(x - 7)

143.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

144.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

145.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

146.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

147.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

148.

Which of the following is a perfect square trinomial?

a)

x² – 18x + 81

b)

x² – 12x + 6

c)

x² + 20x + 40

d)

x² – 12x – 36

149.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

150.

Which of the following is NOT a perfect square trinomial?

a)

x² – 16x + 64

b)

x² – 10x + 20

c)

x² – 28x + 196

d)

x² – 24x + 144

151.

25x²+ 60x + 36

a)

(5x + 6)²

b)

(5x - 6)²

c)

(5x + 18)²

d)

Not a Perfect Square Trinomial

152.

a)

A

b)

B

c)

C

d)

D

153.

x² - 9

a)

(x + 3) (x - 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x - 6)

d)

Can't factor using Diff. of Squares

154.

4a² - 25

a)

(2a + 5) (2a - 5)

b)

(2a - 5) (2a - 5)

c)

(x + 5) (x - 5)

d)

Can't factor using Diff. of Squares

155.

4m² + 49

a)

(2m + 7) (2m - 7)

b)

(2m - 7) (2m - 7)

c)

(m + 7) (m - 7)

d)

Can't factor using Diff. of Squares

156.

q² - 121

a)

(q + 11) (q - 11)

b)

(q - 11) (q - 11)

c)

(q + 11) (q + 11)

d)

Can't factor using Diff. of Squares

157.

r⁴ - q⁴

a)

(r² + q²) (r² - q²)

b)

(r² - q²) (r² - q²)

c)

(r + q) (r - q)

d)

Can't factor using Diff. of Squares

158.

9n² + 1

a)

(3n + 1) (3n - 1)

b)

(3n - 1) (3n - 1)

c)

(n + 3) (n - 3)

d)

Can't factor using Diff. of Squares

159.

r² - 9t²

a)

(r + 3t) (r - 3t)

b)

(r - 3t) (r - 3t)

c)

(3r + t) (3r - t)

d)

Can't factor using Diff. of Squares

160.

w⁴ - 625

a)

(w² + 25) (w² - 25)

b)

(w² - 25) (w² - 25)

c)

(w + 25) (w - 25)

d)

Can't factor using Diff. of Squares

161.

x²+ 81

a)

( x - 9 ) ( x - 9 )

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

Can't factor using Diff. of Squares

162.

Fully Factor the Following
25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

163.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

164.

Complete the formula

a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

165.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

166.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

167.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

168.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

169.

Factor using differencesum/ of cubes. (use your notes!)
a³ + b³

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

170.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

171.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

172.

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF 27X³-343?

a)

DIFFERENCE OF TWO CUBES

b)

DIFFERENCE OF TWO SQUARES

c)

FACTORING BY GCF

d)

SUM OF TWO CUBES

173.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

174.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

175.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

176.

64-27a³

a)

(4-3a)(9a²+12a+16)

b)

(3a-4)(3a²+12a+16)

c)

(4-3a)(3a²+12a+16)

d)

(4-3a)³

177.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

178.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

179.

Complete the formula

a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

180.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

181.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Use the X-Puzzle

182.

Factor completely.

49x² + 16

a)

( 7x + 4 ) ( 7x - 4 )

b)

( 7x + 4 ) ( 7x + 4 )

c)

( 7x - 4 ) ²

d)

cannot be factored (SUM of squares)

183.

∛8

a)

2

b)

4

c)

1

d)

64

184.

∛64

a)

4

b)

5

c)

6

d)

3

185.

∛216

a)

6

b)

7

c)

5

d)

8

186.

∛343

a)

7

b)

6

c)

8

d)

9

187.

∛512

a)

8

b)

7

c)

9

d)

6

188.

A cube has the volume of 343in³. What are the side lengths?

a)

7in

b)

6in

c)

8in

d)

13in

189.

A cube has the volume of 8in³. What are the side lengths?

a)

64in

b)

2in

c)

4in

d)

16in

190.

A cube has side lengths of 4 in. What is the volume?

a)

16in³

b)

64in³

c)

64in²

d)

64in

191.

The number 512 is a perfect cube because 512 = 8³.

Which number below is also a perfect cube?

a)

125

b)

300

c)

150

d)

256

192.

What is 6³ ?

(a)

193.

What is 12³ ?

(a)

194.

What is 4³ ?

(a)

195.

What is ∛27 ?

(a)

196.

Factor x³ - 4x.

a)

(x-4)(x²-4)

b)

x(x-2)(x+2)

c)

x(x-4)

d)

(x-2)(x+2)

197.

Factor Completely:

2n³ + 7n² - 2n - 7

a)

cannot be factored

b)

(n - 1)²(2n + 7)

c)

(n² - 1)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

198.

Factor completely:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

199.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

200.

Factor Completely:
3x⁴ + 3x³ - 12x² - 12x

a)

3x(x³ + x²- 4x - 4)

b)

3x(x²-4)(x+1)

c)

3x(x+2)(x-2)(x+1)

d)

3x(x²+4)(x-1)

201.

What is [ (12x³y⁵z⁷)/ (144x^-4 y⁷z^-3)]⁰

a)

12(x⁷z¹⁰)

b)

(x⁷z¹⁰)/12y²

c)

1

d)

(x⁷y^-2z¹⁰)/12

202.

Simplify: $2^{-4}$

a)

$-8$

b)

$-16$

c)

$-\frac{1}{8}$

d)

$\frac{1}{16}$

203.

$x^{-7}$

a)

$\frac{1}{x^{-7}}$

b)

$\frac{1}{x^7}$

c)

$x^7$

d)

$7x$

204.

Rewrite using a Positive Exponent: $5n^{-9}$

a)

$-5n^9$

b)

$-\frac{5}{n^9}$

c)

$\frac{5}{n^9}$

d)

$-45n$

205.

$\frac{1}{w^{-2}}$

a)

$w^2$

b)

$-2w$

c)

$\frac{2}{w}$

d)

$\frac{1}{w^2}$

206.

Simplify: $x^3\ \cdot\ x^{-3}$

a)

$x^{0\ }=\ \ 1$

b)

$x^{-1\ \ }=\ \ \frac{1}{x}$

c)

$2x^{-9}\ =\ \frac{2}{x^9}$

d)

$2x^0=\ 2$

207.

Simplify: $\frac{x^{-3}}{x^{-7}}$

a)

$x^{21}$

b)

$x^4$

c)

$\frac{1}{x^{21}}$

d)

$\frac{1}{x^{10}}$

208.

$\frac{x^5y^{-6}z}{x^{-3}y^{ }z^{-3}}$

a)

$\frac{x^8z^4}{y^7}$

b)

$\frac{x^2z^3}{y^5}$

c)

$\frac{x^8}{y^7z^4}$

d)

$\frac{x^2}{y^5z^2}$

209.

How would you change this to a positive exponent:
1/x^-3

a)

1/x³

b)

x³

c)

3x

d)

1/3x

210.

x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

211.

-3xy³ . (4xy)²

a)

-12x³y⁵

b)

-48x²y⁴

c)

-48x³y⁵

d)

-12x²y⁶

212.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

213.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

214.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

215.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

216.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

$4v^{\frac{1}{3}}$

b)

$\frac{4}{v^{\frac{1}{3}}}$

c)

$\frac{v^{\frac{1}{3}}}{4}$

d)

$\frac{1}{4v^{\frac{1}{3}}}$

217.

Simplify . Your answer should contain only positive exponents. $\left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1}$

a)

$\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

b)

$a^{\frac{1}{2}}b^{\frac{1}{2}}$

c)

$-\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$

d)

$-a^{\frac{1}{2}}b^{\frac{1}{2}}$

218.

Simplify . Your answer should contain only positive exponents. $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

219.

Simplify . Your answer should contain only positive exponents. $\frac{a^2b^0}{3a^4}$

a)

$1$

b)

$\frac{1}{3a^2}$

c)

$\frac{a^2}{3a^4}$

d)

$\frac{1}{3a^4}$

220.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

221.

Simplify . Your answer should contain only positive exponents. $\left(x^0y^{\frac{1}{3}}\right)^{\frac{3}{2}}x^0$

a)

$y^{\frac{1}{2}}$

b)

$1$

c)

$y^{\frac{4}{3}}$

d)

$0$

222.

Simplify . Your answer should contain only positive exponents. $\frac{a^{\frac{3}{4}}b^{-1}\cdot b^{\frac{7}{4}}}{3b^{-1}}$

a)

$\frac{a^{\frac{3}{4}}b^{\frac{7}{4}}}{3}$

b)

$\frac{a^{\frac{3}{4}}b^{\frac{3}{4}}}{3}$

c)

$a^{\frac{3}{4}}b^{\frac{7}{4}}$

d)

$3a^{\frac{3}{4}}b^{\frac{7}{4}}$

223.

Simplify . Your answer should contain only positive exponents. $u^{-\frac{5}{4}}v^2•\left(u^{\frac{3}{2}}\right)^{-\frac{3}{2}}$

a)

$\frac{v^2}{u^{\frac{7}{2}}}$

b)

$\frac{v^2}{u^{\frac{5}{2}}}$

c)

$\frac{v^2}{u^{\frac{5}{4}}}$

d)

$v^2$

224.

Simplify . Your answer should contain only positive exponents. $\frac{3y^{-\frac{5}{4}}}{y^{-1}•2y^{-\frac{1}{3}}}$

a)

$\frac{3y^{\frac{1}{12}}}{2}$

b)

$\frac{3y^{\frac{19}{12}}}{2}$

c)

$\frac{3}{2y^{\frac{1}{12}}}$

d)

$\frac{3}{2y^{\frac{19}{12}}}$

225.

Simplify . Your answer should contain only positive exponents. $\frac{\left(m^2n^{\frac{1}{2}}\right)^0}{n^{\frac{3}{4}}}$

a)

$1$

b)

$n^{\frac{3}{4}}$

c)

$\frac{1}{n^{\frac{3}{4}}}$

d)

$\frac{1}{n^{\frac{4}{3}}}$

226.

Simplify . Your answer should contain only positive exponents. $\left(6b\right)^{\frac{-4}{3}}$

a)

$\frac{1}{6^{\frac{4}{3}}b^{\frac{4}{3}}}$

b)

$\frac{6}{b^{\frac{4}{3}}}$

c)

$\frac{b^{\frac{4}{3}}}{6}$

d)

$\frac{6^{\frac{4}{3}}}{b^{\frac{4}{3}}}$

227.

Classify the following polynomial

a)

quartic polynomial

b)

quadratic polynomial

c)

quartic trinomial

d)

quadratic trinomial

228.

______________________________ arranges the terms by degree in descending numerical order.

a)

degree of polynomial

b)

polynomial

c)

terms

d)

standard form of polynomial

229.

Is this expression in Standard Form?
6w² - 9w³

a)

Yes

b)

No

230.

What is the degree?
- 3x³ - x² - 10x + 12

a)

1

b)

2

c)

3

d)

4

231.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

232.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

233.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

234.

Classify by number of terms:
3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

235.

Classify by degree of polynomial:
3x² – 8x + 1

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

236.

Classify by number of terms:
12

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

237.

Classify by degree of polynomial:
12

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

238.

Classify by degree of polynomial:
7x³ – 8x² -4x+ 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

239.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

240.

What is the leading coefficient?
f(x)=5x²+3x³-2x+1

a)

5

b)

3

c)

-2

d)

1

241.

When a polynomial is written in standard form, the coefficient of the first term is called the _____________.

a)

Boss coefficient

b)

Leading coefficient

c)

Best coefficient

d)

Greatest common coefficient

242.

What is the constant in the polynomial x²-2x+5?

a)

1

b)

2

c)

5

d)

0

243.

What is the correct name of the following:
3xy + 4x + 5y + 6

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

244.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

245.

Which of these is in Standard Form?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

246.

Which polynomial is written in standard form?

a)

8x - 11x²

b)

4x³ + 7x - 9

c)

12 + 4x

d)

13x + 7x² - 9x³ + 12

247.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

248.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

249.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

250.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

251.

Classify by number of terms:
3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

252.

Classify by degree of polynomial:
3x² – 8x + 1

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

253.

Classify by number of terms:
12

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

254.

Classify by number of terms:
7x³ – 8x² + 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

255.

Classify by degree and number of terms:

3x³ – 6x

a)

Quadratic Binomial

b)

Cubic Binomial

c)

Cubic Trinomial

d)

4th degree Binomial

256.

Classify the polynomial by degree and number of terms:

3x² – 8x + 1

a)

Cubic Trinomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Quadratic Binomial

257.

Name of polynomial with 3 terms

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

258.

What is the name of 1 term?

a)

Trinomial

b)

binominal

c)

term

d)

monomial

259.

Classify by degree and number of terms:

$4$

a)

quartic monomial

b)

constant monomial

c)

linear monomial

d)

constant polynomial

260.

Classify by degree and number of terms:

$7x$

a)

linear binomial

b)

linear monomial

c)

constant monomial

d)

constant binomial

261.

Classify by degree and number of terms:

$5y^3-8y$

a)

cubic monomial

b)

quadratic polynomial

c)

cubic binomial

d)

quadratic trinomial

262.

Classify by degree and number of terms:

$x^2+3x-9$

a)

quadratic trinomial

b)

cubic trinomial

c)

quadratic binomial

d)

cubic polynomial

263.

Classify the following by degree:

$2x^5+3$

a)

Linear

b)

5th degree or Quintic

c)

quadratic

d)

constant

264.

Classify the following by degree:

$x^{10}+y+5$

a)

10th degree

b)

cubic

c)

qudratic

d)

linear

265.

Nam by number of terms:

x

a)

monomial

b)

binomial

c)

trinomial

266.

Name by the number of terms:

$x^2+y^3-z^4+3$

a)

monomial

b)

4-term polynomial or just polynomial

c)

trinomial

d)

binomial

Factoring and exponents

Total questions: 266

Worksheet time: 19hrs 15mins

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