Free Printable Algebra 22.01.2022

1.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

2.

Factor by using GCF:
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

3.

3x³+ 9x²- 15x

a)

x(3x² + 9x - 15)

b)

3x(x² + 3x - 5)

c)

3x(x² - 9x + 15)

d)

x(3x² -9x + 15)

4.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

5.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

6.

Factor:
2n²+16n+12

a)

2n(n²+24n+6)

b)

2(n²+8n+6)

c)

2n(n²+8n+6)

d)

3(n²+8n+6)

7.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

8.

What is the GCF? 3x²-2x

a)

3

b)

3x

c)

x

d)

2

9.

Factor the polynomial
32y³ + 8y²

a)

8y²

b)

8y(4y² + y)

c)

8y²(4y + 1)

d)

8y²(4y + 8)

10.

Factor
5ab²c¹¹ + 2bc⁵

a)

bc⁵(5ab²c⁶ + 2b)

b)

bc⁵(5abc⁶ + 2)

c)

b²c⁵(5bc⁶ + 2)

d)

c4(5a²b²c⁷+ 2bc)

11.

w³ + 3w

a)

3w(1)

b)

w(w² + 3)

c)

w³(w + 3)

12.

4x + 6

a)

4(x + 2)

b)

2(2x + 3)

c)

2(2x + 4)

d)

4(x + 2/3)

13.

8r³ + 16r²

a)

4r²(2r + 4)

b)

8r²(r + 2)

c)

8(r³ + r²)

d)

4(r³ + 2r²)

14.

Factor:

7x+49

a)

$7x\left(x+49\right)$

b)

$7\left(x+7\right)$

c)

$49\left(x+7\right)$

d)

$x\left(7+49\right)$

15.

Factor:
$5a^2-15$

a)

$5\left(a^2-15\right)$

b)

$5a\left(a-15\right)$

c)

$5\left(a^2-3\right)$

d)

$5a\left(a-3\right)$

16.

When did Ms. Manzoor get married?

a)

30 years ago

b)

Never

c)

100 years ago

d)

December break

17.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

18.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

19.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

20.

Fill in the blank: Who lives in a pinneapple under the sea ___________________________________

a)

Spongebob Square Pants

b)

Mr. Kraby

c)

Plankton

d)

Patrick Star

21.

Factor
18a²b⁴c + 24ab³c²

a)

6ab³c(3ab + 4c)

b)

3abc(6ab³+ 8b²c)

c)

6abc(3ab³ + 4c)

d)

6ab3c(3b + 4c)

22.

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

a)

x²

b)

x²y²z

c)

x²y²

d)

x⁵y⁷z

23.

Factor
5ab²c¹¹ + 2bc⁵

a)

bc⁵(5ab²c⁶ + 2b)

b)

bc⁵(5abc⁶ + 2)

c)

b²c⁵(5bc⁶ + 2)

d)

c4(5a²b²c⁷+ 2bc)

24.

Factor
12j²k³ - 20hj

a)

4j(3jk³ - 5h)

b)

4j(6jk³ - 10h)

c)

4j(3jk² - 5h)

d)

4j²(24j²k³ - 20h)

25.

Factor
20p²q² - 25pm

a)

pm(4q - 5m)

b)

5(4pq³ - 5m)

c)

pq(20pq² - 25m)

d)

5p(4pq² - 5m)

26.

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

a)

4mn

b)

24mn⁴

c)

4mn⁴

d)

4mn⁴p

27.

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)

28.

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

a)

9xy

b)

-9

c)

9x

d)

xy

29.

Factor
25a⁴b⁴ + 25a³b³ + 25a²b²

a)

25a⁴b⁴(ab + a²b² + 25)

b)

a²b²(25a²b² + 25ab + 25)

c)

25a²b²(a²b² + ab + 1)

d)

25a²b²(a²b² + ab + ab)

30.

Factor
500x³y³ + 1000x²y² + 1500xy

a)

500xy(x²y² + 2xy + 3)

b)

1500x³y³(3 + 2xy + xy)

c)

500xy(x²y² +500xy + 1000)

d)

500xy(x³y³ + x²y² + xy)

31.

(7r+6)(7r+6)

a)

49r²+36

b)

49r²-36

c)

49r²+84r+36

d)

49r²+42r+36

32.

(3m + 1)(3m – 1)

a)

9m²– 1

b)

9m²– 6m – 1

c)

9m²+ 1

d)

9m²+ 6m – 1

33.

(6x+y)(6x-y)

a)

6x²+y²

b)

18x²-3x+3x-xy+xy-1

c)

36x²+6x-6xy+y²

d)

36x²-y²

34.

(x + 4)²

a)

x² + 4x + 16

b)

x² + 8x + 16

c)

x² + 8x + 8

d)

x² - 8x + 16

35.

(2x + 5)²

a)

4x² + 20x + 25

b)

x² + 20x + 25

c)

4x² + 20x + 10

d)

2x² + 20x + 25

36.

Multiply
(4x-3)²

a)

16x²-24x+9

b)

16x² - 9

c)

16x² + 9

d)

16x²⁺24x+9

37.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

d)

r − 49

38.

Multiply
(3x-5)(3x+5)

a)

9x²-30x-25

b)

6x²-30x-25

c)

9x²-25

d)

6x²+25

39.

(x+3)²

a)

x²

b)

x²-6x-9

c)

x²+6x+9

d)

3x²+6x+9

40.

(6x+5)²

a)

36x+60x+25

b)

36x²+60x+25

c)

60x+25

d)

x²

41.

Find the product

\left(x+7\right)^2

a)

$x^2+49$

b)

$x^2+7x+49$

c)

$x^2+14x+49$

d)

$x^2+49x+14$

42.

Find the product

\left(2w-3\right)^2

a)

$4w^2-12w+9$

b)

$4w^2+9$

c)

$4w^2-9$

d)

$4w^2+12w-9$

43.

Find the product

\left(n+4\right)\left(n-4\right)

a)

$n^2-8n+16$

b)

$n^2+8n-16$

c)

$n^2+16$

d)

$n^2-16$

44.

Find the product

\left(5x+2\right)\left(5x-2\right)

a)

$10x^2-4$

b)

$25x^2-4$

c)

$25x^2-20x-4$

d)

$10x^2+20x-4$

45.

Find the product

\left(6+a\right)\left(6-a\right)

a)

$36-12a-a^2$

b)

$a^2-36$

c)

$36-a^2$

d)

$a^2-12a-36$

46.

Find the product

\left(x+2y\right)\left(x-2y\right)

a)

$x^2-4y^2$

b)

$x^2-2y^2$

c)

$x^2-4xy-4y^2$

d)

$x^2-4xy-2y^2$

47.

The dimensions of a room are

\left(x+3\right)

by

\left(x+3\right)

. Find the area of the room.

a)

$x^2+6x+9$

b)

$x^2+9$

c)

$2x+6$

d)

$4x+12$

48.

The area of a house after a renovation is $\left(x+20\right)^2$ . Find this product.

a)

$x^2+20x$

b)

$2x+40$

c)

$x^2+400$

d)

$x^2+40x+400$

49.

$\left(x+6\right)^2$

Which choice is NOT equivalent to

a)

$\left(x+6\right)\left(x+6\right)$

b)

$x^2+6x+6x+36$

c)

$x^2+12x+36$

d)

$x^2+36$

50.

Find the area of the square.

a)

$9x^2+4$

b)

$6x+4$

c)

$9x^2+12x+4$

d)

$6x^2+9x+12$

51.

Find the product.

(x + 4)(x - 4)

a)

x² -16

b)

x² +16

c)

x² - 8x -16

d)

x² - 8x +16

52.

(7r-6)(7r+6)

a)

49r²+36

b)

49r²-36

c)

49r²+84r+36

d)

49r²+42r+36

53.

(u-5v)(u+5v)

a)

u²-25v²

b)

u²+25v²

c)

u²-10uv+25v²

d)

u²+10uv+25v²

54.

(2u-4v)²

a)

4u²-8uv+16v²

b)

4u²-16uv+16v²

c)

4u²-16v²

d)

4u²+8uv+16v²

55.

(10x+12y)²

a)

100x²+120xy+144y²

b)

100x²+240xy+144y²

c)

20x²+120xy+24y²

d)

20x²+120xy+144y²

56.

a)

A

b)

B

c)

C

d)

D

57.

Simplify:
(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

58.

(11 - x)²

a)

x² - 22x + 121

b)

x² - 10x + 22

c)

x² + 22 x - 22

d)

x² + 11x + 121

59.

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

a)

9x² -24 x + 16

b)

9x² -12 x + 16

c)

12x² -12 x + 12

d)

12x² -7x + 12

60.

(g - 4h) (g - 4h)

a)

g² - 8gh + 16h²

b)

g² - 3gh + 16h²

c)

g² - 6gh + 16h²

d)

2g² - 8gh + 8h²

61.

(3c + 6d)²

a)

9c² + 36cd + 36d²

b)

9c² + 18cd + 36d²

c)

6c² + 36cd + 12d²

d)

6c² + 9cd + 12d²

62.

(x + 5)²

a)

x² + 10x + 25

b)

x² + 5x + 25

c)

x² + 6x - 10

d)

x² _6x + 25

63.

(x - 3 ) (x + 3)

a)

x² - 6x + 9

b)

x² - 9x + 6

c)

x² - 12x - 6

d)

x² - 9

64.

(x + 5) (x - 5)

a)

x² -10x + 25

b)

x² - 25x - 25

c)

x² - 50x + 25

d)

x² - 25

65.

(2u-4v)²

a)

4u²-8uv+16v²

b)

4u²-16uv+16v²

c)

4u²-16v²

d)

4u²+8uv+16v²

66.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

67.

Find the slope (remember: change in y/change in x)

a)

1/3

b)

3

c)

-3

d)

-1

68.

WRITE AN EQUATION

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

a)

24-10=7x

b)

24+7x=10

c)

10+7x=24

d)

10+x=14

69.

WRITE AN EQUATION
Imani spent half of her weekly allowance playing mini-golf. To earn more money her parents let her wash the car for $4. What is her weekly allowance if she ended with $12?

a)

0.5x+4=12

b)

x+4=12

c)

12-4=x

d)

12-4=0.5x

70.

The first play of a football game resulted in a loss of 12 yards. Then a penalty resulted in another loss of 5 yards. What is the total loss or gain?

a)

a gain of 7 yards

b)

a loss of 7 yards

c)

a gain of 17 yards

d)

a loss of 17 yards

71.

Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.

a)

7x + 35 = 63

b)

7x = 63

c)

7x - 35 = 63

d)

35x + 7 = 63

72.

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she spends $35 in all.

a)

.50x + 20 = 35

b)

.50x = 35

c)

.50 + 20x = 35

d)

.50x - 20 = 35

73.

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage. If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

a)

C = 0.20x + 15

b)

C =15 (0.20x)

c)

C = 15 + x + 0.20

d)

C = 0.20 + 15x

74.

A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear. They sell the teddy bears for $12 a piece. Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?

a)

1500 + 8t = 12

b)

12 + 8t = 1500

c)

1500 + 8t = 12t

d)

8t = 12t + 1500

75.

WRITE AN EQUATION
For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

a)

4x=472

b)

9x=472

c)

4+9x=472

d)

4+x=472

76.

Jason says that 10 less than one third of his age is 11 years old. How old is Jason?

a)

3 years old

b)

7 years old

c)

57 years old

d)

63 years old

77.

Maria has 25 dollars. She has to buy a gallon of milk which costs $3.50. She wants to spend the rest of her money on cereal. If each box of cereal costs $4.50, how many can she purchase?

a)

4 boxes

b)

5 boxes

c)

6 boxes

d)

7 boxes

78.

Is the sequence arithmetic: -3, 3, -3, 3, ...

a)

Yes

b)

No

79.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

80.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

81.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

82.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

83.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

84.

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

a)

-20, -24, -28

b)

-21, -25, -29

c)

-23, -28, -33

d)

-24, -29, -32

85.

Select the explicit rule that represents the sequence.

a)

6 + 5(n - 1)

b)

4 + 6(n - 1)

c)

6 - 4(n - 1)

86.

Find the 22nd term of the following sequence:

5, 8, 11, ...

(Hint: Write the explicit rule first, then use it to solve)

a)

14

b)

68

c)

63

d)

71

87.

Find the 32nd term of this sequence.

34, 37, 40, 43, ...

(Hint: Write the explicit rule first, then use it to solve)

a)

32

b)

64

c)

127

d)

356

88.

Given the sequence:

25, 21, 17, 13,...

Write the explicit equation that models the sequence.

a)

a_n = 25 + 4(n - 1)

b)

a_n = 29 - 4(n - 1)

c)

a_n= 25 - 4(n - 1)

d)

a_n = 29 + 4(n - 1)

89.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

90.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

91.

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

a)

-1.2

b)

1.3

c)

1.2

d)

-1.3

92.

For the sequence shown below, write the explicit formula then find the 57^th term. What is the 57^th term?

a)

-266

b)

-265

c)

-267

d)

-260

93.

What method should you use to factor the polynomial?

5n³-10n²+3n-6

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Master Product

94.

What method should you use to factor the polynomial?

8r³ - 16r²

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Master Product

95.

Factor Completely:

x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

96.

What is the factored form of 5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

97.

Factor Completely.
$8x^2-200$

a)

$8\left(x+5\right)\left(x-5\right)$

b)

$8\left(x^2-25\right)$

c)

$4\left(2x^2-50\right)$

d)

$4\left(2x+25\right)\left(2x-25\right)$

98.

Which of the following is one of the factors of the expression: $4x^2-25?$

a)

$\left(4x-5_{ }\right)$

b)

$\left(2x+1\right)$

c)

$\left(4x-1\right)$

d)

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

99.

What is the factored form of the expression? $x^2-16$

a)

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

b)

$\left(x-8\right)\left(x+8\right)$

c)

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

d)

$\left(x-8\right)\left(x-8\right)$

100.

Which shows the polynomial $8x^2+16x+8$ completely factored?

a)

$\left(4x+4\right)^2$

b)

$\left(4x+4\right)\left(2x+2\right)$

c)

$8\left(x+1\right)^2$

d)

$8\left(x+1\right)\left(x-1\right)$

101.

When factored completely, $x^3-9x$ is equivalent to:

a)

$x\left(x-3\right)$

b)

$x\left(x+3\right)\left(x-3\right)$

c)

$\left(x+3\right)\left(x-3\right)$

d)

$x\left(x+3\right)$

102.

Which expression is the factored form of $2x^2-2x-12?$

a)

$2\left(x+2\right)\left(x-3\right)$

b)

$2\left(x+6\right)\left(x-1\right)$

c)

$2\left(x+3\right)\left(x-2\right)$

d)

$2\left(x+1\right)\left(x-6\right)$

103.

If $\left(x-3\right)$ and $\left(x+7\right)$ are the factors of the trinomial $x^2+bx-21$ , what is the value of b?

a)

$-3$

b)

$-4$

c)

$7$

d)

$4$

104.

If $\left(2x-3\right)$ and $\left(x+5\right)$ are multiplied to form the trinomial $ax^2+bx+c$ , what is the value of b?

a)

$-15$

b)

$2$

c)

$7$

d)

$4$

105.

Factor the trinomial completely. $x^2-x-30$

a)

$\left(x+1\right)\left(x-30\right)$

b)

$\left(x+5\right)\left(x-6\right)$

c)

$\left(x+6\right)\left(x-5\right)$

d)

$prime$

106.

Factor the trinomial completely. $x^2-6x-72$

a)

$\left(x-12\right)\left(x+6\right)$

b)

$\left(x-72\right)\left(x+1\right)$

c)

$\left(x+12\right)\left(x-6\right)$

d)

$prime$

107.

Factor the binomial completely. $36-25x^2$

a)

$\left(6-5x\right)^2$

b)

$\left(6+5x\right)^2$

c)

$\left(6+5x\right)\left(6-5x\right)$

d)

$prime$

108.

What is the factored form of the expression? $x^2+x-6$

a)

$\left(x-3\right)\left(x+2\right)$

b)

$\left(x+1\right)\left(x-6\right)$

c)

$\left(x-2\right)\left(x+3\right)$

d)

$\left(x-2\right)\left(x-3\right)$

109.

What are the binomial factors of $x^2+7x-18$

(Pick 2 answers)

a)

$\left(x-9\right)$

b)

$\left(x+9\right)$

c)

$\left(x-2\right)$

d)

$\left(x+2\right)$

110.

Which is a factor of $x^2-11x+24?$

a)

$\left(x+3\right)$

b)

$\left(x-3\right)$

c)

$\left(x+4\right)$

d)

$\left(x-4\right)$

111.

If $\left(x-3\right)$ is a factor of $x^2+x-12$ , then the other factor is?

a)

$\left(4x-3\right)$

b)

$\left(3x-4\right)$

c)

$\left(x-4\right)$

d)

$\left(x+4\right)$

112.

Written in factored form, the trinomial $2y^2+26y+80$ is equivalent to:

a)

$2\left(y-5\right)\left(y-8\right)$

b)

$\left(2y+5\right)\left(y+8\right)$

c)

$2\left(y+5\right)\left(y+8\right)$

d)

$\left(y+5\right)\left(2y+16\right)$

Algebra 22.01.2022

Total questions: 112

Worksheet time: 5hrs 18mins

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