Free Printable U4 - Polynomial Operations (2025)

1.

Simplify. Write your answer in standard form.

$6x\left(3x^2+4x\right)-5x\left(7x-2\right)$

2.

Find the area of the shaded region. Write your answer in standard form. Do not type a= or x= etc.

3.

Simplify. Write your answer in standard form.

$8x\left(3x^2+4x\right)+5\left(6x-7\right)$

4.

Simplify. Write your answer in standard form.

$9x\left(3x^2-10\right)+5\left(6x+7\right)$

5.

Simplify. Write your answer in standard form.

$4x\left(6x-3\right)-9\left(8x-5\right)$

6.

Simplify. Write your answer in standard form.

$3x\left(5x-6\right)-4\left(7x-2\right)$

7.

Simplify. Write your answer in standard form.

$6x\left(4x-7\right)-2\left(8x-5\right)$

8.

Simplify. Write your answer in standard form.

$5x^2\left(9x-3\right)+4\left(6x+7\right)$

9.

Simplify. Write your answer in standard form.

$2x\left(7x^2+8x\right)-4\left(5x+9\right)$

10.

Find the area of the shaded region. Write your answer in standard form. Do not type a= or x= etc.

11.

Simplify. Write your answer in standard form.

$4x\left(5x^2-7x+11\right)$

12.

Simplify. Write your answer in standard form.

$\left(4x\right)+\left(5x^2-7x+11\right)$

13.

Simplify. Write your answer in standard form.

$\left(4x\right)-\left(5x^2-7x+11\right)$

14.

Simplify. Write your answer in standard form.

$\left(3x+7\right)\left(4x-5\right)$

15.

Simplify. Write your answer in standard form.

$\left(4x^2+3\right)\left(2x+9\right)$

16.

Simplify. Write your answer in standard form.

$\left(4x^2+3\right)+\left(2x+9\right)$

17.

Simplify. Write your answer in standard form.

$\left(4x-5\right)\left(6x-7\right)$

18.

Simplify. Write your answer in standard form.

$\left(3x^2+7\right)\left(4x-5\right)$

19.

Find the area of the larger rectangle.

Write your answer in standard form. Do not type a= or p= etc.

20.

Find the perimeter of the larger rectangle.

Write your answer in standard form. Do not type p= or a= etc.

21.

Find the perimeter of the smaller rectangle.

Write your answer in standard form. Do not type p= or a= etc.

22.

Find the area of the smaller rectangle. Write your answer in standard form. Do not type p= or a= etc.

23.

Simplify. Write your answer in standard form.

$\left(4x+7\right)-\left(3x^2-5x-9\right)$

24.

Simplify. Write your answer in standard form.

$\left(4x+7\right)\left(3x^2-5x-9\right)$

25.

Simplify. Write your answer in standard form.

$\left(3x+5\right)\left(2x^2-6x-7\right)$

26.

Simplify. Write your answer in standard form.

$\left(3x+5\right)+\left(2x^2-6x-7\right)$

27.

Find the area of the rectangle. Write your answer in standard form. Do not type a= or x= etc.

28.

Find the area of the rectangle. Write your answer in standard form. Do not type a= or x= etc.

29.

Find the perimeter of the rectangle. Write your answer in standard form. Do not type p= or x= etc.

30.

Find the area of the rectangle. Write your answer in standard form. Do not type a= or x= etc.

31.

Find the perimeter of the rectangle. Write your answer in standard form. Do not type p= or x= etc.

32.

Factor. Write your answer in standard form.

$30x^6+24x^5-18x^4$

33.

Factor. Write your answer in standard form.

$8x^5+9x^4+11x^3$

34.

Factor. Write your answer in standard form.

$7x^8+x^6+4x^5$

35.

Factor. Write your answer in standard form.

$12x^2+8x+16$

36.

Factor. Write your answer in standard form.

$30x^2+20x+70$

37.

Factor. Write your answer in standard form.

$24x^5+12x^4+18x$

38.

Factor. Write your answer in standard form.

$16x^7+32x^5+24x^3$

39.

Factor. Write your answer in standard form.

$12x^6+9x^4-15x^2$

40.

Simplify. Write your answer in standard form.

$\left(4x^2+5x-10\right)-\left(x^2+3x-7\right)$

41.

Simplify. Write your answer in standard form.

$\left(9x^3-4x^2-8x\right)-\left(2x^3-7x^2-17x\right)$

42.

Simplify. Write your answer in standard form.

$5x\left(3x^2+4x-9\right)$

43.

Simplify. Write your answer in standard form.

$\left(5x-2\right)\left(4x-9\right)$

44.

Simplify. Write your answer in standard form.

$\left(3x^2-6\right)\left(2x-7\right)$

45.

Simplify. Write your answer in standard form.

$\left(3x^2-6\right)+\left(2x-7\right)$

46.

Simplify. Write your answer in standard form.

$\left(3x^2-6\right)-\left(2x-7\right)$

47.

Simplify. Write your answer in standard form.

$\left(5x-2\right)+\left(4x-9\right)$

48.

Simplify. Write your answer in standard form.

$\left(5x\right)+\left(3x^2+4x-9\right)$

49.

Simplify. Write your answer in standard form.

$3\left(5x^2-6x\right)-7\left(2x-3\right)$

50.

Simplify. Write your answer in standard form.

$7x\left(4x-5\right)-8\left(2x-9\right)$

51.

Factor. Write your answer in standard form.

$13x^7-11x^5+17x$

52.

Factor. Write your answer in standard form.

$15x^5-16x^3+14x^2$

53.

Factor

a)

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

1.

$x^2 + 9x + 20$

b)

$\left(x+2\right)\left(x+10\right)$

2.

$x^2 + 12x + 20$

c)

$\left(x+1\right)\left(x+20\right)$

3.

$x^2 + 21x + 20$

d)

$\left(x-2\right)\left(x-10\right)$

4.

$x^2-12x+20$

e)

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

5.

$x^2-9x+20$

54.

Factor. Do not type spaces.

$x^2+13x+12$

(a)

55.

Factor. Do not type spaces.

$x^2+8x+12$

(a)

56.

Factor. Do not type spaces.

$x^2+7x+12$

(a)

57.

Factor. Do not type spaces.

$x^2+x-12$

(a)

58.

Factor. Do not type spaces.

$x^2-x-12$

(a)

59.

Factor. Do not type spaces.

$x^2-11x-12$

(a)

60.

Factor. Do not type spaces.

$x^2+11x-12$

(a)

61.

Factor. Do not type spaces.

$x^2-7x+12$

(a)

62.

Factor. Do not type spaces.

$x^2+8x+15$

(a)

63.

Factor. Do not type spaces.

$x^2-8x+15$

(a)

64.

Factor. Do not type spaces.

$x^2-2x-15$

(a)

65.

Factor. Do not type spaces.

$x^2+2x-15$

(a)

66.

Factor. Do not type spaces.

$x^2+12x+20$

(a)

67.

Factor. Do not type spaces.

$x^2-12x+20$

(a)

68.

Factor. Do not type spaces.

$x^2-8x-20$

(a)

69.

Factor. Do not type spaces.

$x^2+8x-20$

(a)

70.

Match the following

a)

$x^2+25x+24$

1.

(x+1)(x+24)

b)

$x^2+14x+24$

2.

(x+2)(x+12)

c)

$x^2+11x+24$

3.

(x+3)(x+8)

d)

$x^2+10x+24$

4.

(x+4)(x+6)

e)

$x^2+250x+24$

5.

not factorable

71.

Match the following

a)

$x^2+7x-18$

1.

(x-2)(x+9)

b)

$x^2-7x-18$

2.

(x+2)(x-9)

c)

$x^2-300x-18$

3.

not factorable

d)

$x^2-17x-18$

4.

(x+1)(x-18)

e)

$x^2+17x-18$

5.

(x-1)(x+18)

72.

Match the following

a)

$x^2+8x+15$

1.

(x+3)(x+5)

b)

$x^2-8x+15$

2.

(x-3)(x-5)

c)

$x^2-16x+15$

3.

(x-1)(x-15)

d)

$x^2+16x+15$

4.

(x+1)(x+15)

e)

$x^2-123x+15$

5.

not factorable

73.

Match the following

a)

$x^2-7x+10$

1.

(x-2)(x-5)

b)

$x^2+7x+10$

2.

(x+2)(x+5)

c)

$x^2-3x-10$

3.

(x+2)(x-5)

d)

$x^2+3x-10$

4.

(x-2)(x+5)

e)

$x^2-70x+10$

5.

not factorable

74.

Factor. Do not type spaces.

$x^3+100x^2+12x$

75.

Factor. Do not type spaces.

$5x^2+500x+50$

76.

Factor. Do not type spaces.

$7x^3+700x^2+70x$

77.

Factor

a)

$x^2-11x-12$

1.

(x-12)(x+1)

b)

$x^2+11x-12$

2.

(x+12)(x-1)

c)

$x^2-x-12$

3.

(x-4)(x+3)

d)

$x^2+x-12$

4.

(x+4)(x-3)

e)

$x^2-600x-12$

5.

not factorable

78.

Factor

a)

$x^2-2x-15$

1.

(x-5)(x+3)

b)

$x^2+2x-15$

2.

(x+5)(x-3)

c)

$x^2-14x-15$

3.

(x-15)(x+1)

d)

$x^2+14x-15$

4.

(x+15)(x-1)

e)

$x^2-1200x-15$

5.

not factorable

79.

Factor

a)

$x^2-x-20$

1.

(x-5)(x+4)

b)

$x^2+x-20$

2.

(x+5)(x-4)

c)

$x^2-8x-20$

3.

(x-10)(x+2)

d)

$x^2+8x-20$

4.

(x+10)(x-2)

e)

$x^2+3x-20$

5.

not factorable

80.

Factor

a)

$x^2+17x+16$

1.

(x + 1)(x + 16)

b)

$x^2-17x+16$

2.

(x - 1)(x - 16)

c)

$x^2-15x-16$

3.

(x - 16)(x + 1)

d)

$x^2+15x-16$

4.

(x + 16)(x - 1)

e)

$x^2+500x+16$

5.

not factorable

81.

Factor

a)

$x^2+12x+11$

1.

(x + 11)(x + 1)

b)

$x^2-12x+11$

2.

(x - 11)(x - 1)

c)

$x^2+10x-11$

3.

(x + 11)(x - 1)

d)

$x^2-10x-11$

4.

(x - 11)(x + 1)

e)

$x^2+800x-11$

5.

not factorable

82.

Factor

$y^2+16$

a)

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

b)

$\left(y+4\right)\left(y+4\right)$

c)

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

d)

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

e)

not factorable

83.

Factor

$y^2+8y+16$

a)

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

b)

$\left(y+4\right)\left(y+4\right)$

c)

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

d)

$\left(y+1\right)\left(y+16\right)$

e)

Not factorable

84.

Factor.

$25x^2-36$

Do not type spaces.

(a)

85.

Factor

$81x^2-1$

Do not type spaces

(a)

86.

What is the answer to b?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

87.

What is the answer to c?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

88.

What is the answer to d?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

89.

What is the answer to e?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

90.

What is the answer for b?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

91.

What is the answer for c?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

92.

What is the answer for d?

a)

i

b)

ii

c)

iii

d)

iv

e)

v

93.

Factor

$9-x^2$

Do not type spaces.

(a)

94.

Factor

$x^2-4x-12$

Do not type spaces

(a)

95.

Factor

$x^2-9x+20$

Do not type spaces

(a)

96.

Factor

$12x^5-18x^4$

97.

Factor

$25x^7-30x^5+15x$

98.

Factor

$x^2+8x+16$

Do not type spaces

(a)

99.

Factor

$x^2+18x+81$

Do not type spaces.

(a)

100.

Match the following

a)

$x^2-25$

1.

(x+5)(x-5)

b)

$x^2+25$

2.

not factorable

c)

$x^2-10x+25$

3.

(x-5)(x-5)

d)

$25-x^2$

4.

(5+x)(5-x)

e)

$x^2+10x+25$

5.

(x+5)(x+5)

101.

Match the following

a)

$x^2-121$

1.

(x+11)(x-11)

b)

$121-x^2$

2.

(11+x)(11-x)

c)

$x^2+121$

3.

not factorable

d)

$x^2-22x+121$

4.

(x-11)(x-11)

e)

$x^2+22x+121$

5.

(x+11)(x+11)

102.

Match the following

a)

$x^2-9$

1.

(x+3)(x-3)

b)

$9-x^2$

2.

(3+x)(3-x)

c)

$x^2+9$

3.

not factorable

d)

$x^2-6x+9$

4.

(x-3)(x-3)

e)

$x^2+6x+9$

5.

(x+3)(x+3)

103.

Match the following

a)

$x^2-81$

1.

(x+9)(x-9)

b)

$81-x^2$

2.

(9+x)(9-x)

c)

$x^2+81$

3.

not factorable

d)

$x^2-18x+81$

4.

(x-9)(x-9)

e)

$x^2+18x+81$

5.

(x+9)(x+9)

104.

Factor

$5x^7-150x^4+30x^2$

105.

Match the following

a)

$x^{2\ }+16$

1.

Not factorable

b)

$x^2-16x$

2.

$x\left(x-16\right)$

c)

$x^2-16$

3.

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

d)

$x^2-6x-16$

4.

$\left(x+2\right)\left(x-8\right)$

e)

$x^2+16x$

5.

$x\left(x+16\right)$

106.

Factor

$12x^5-6x^4$

107.

Factor

$16x^2+4$

108.

Factor

$16x^2+9$

a)

not factorable

b)

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

c)

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

d)

$\left(8x+3\right)\left(8x-3\right)$

e)

$x\left(16x+9\right)$

109.

Simplify

$6\left(3x-7\right)-9\left(5x-8\right)$

110.

Factor. Do not type spaces

$10x^3-490x$

(a)

111.

Factor. Do not type spaces

$10x^3+490x$

112.

Factor. Do not type spaces.

3x² + 18x +15

(a)

113.

Factor.

3x⁵ - 27x³

a)

3(x³ - 3)(x²+ 3)

b)

3x³(x + 3)(x + 3)

c)

3x³(x² - 9)

d)

3x³(x - 3)(x + 3)

e)

Not factorable

114.

Factor. Do not type spaces

2x² + 14x +24

(a)

115.

Factor. Do not type spaces.

2x²- 14x - 60

(a)

116.

Factor. Do not type spaces.

8x³ - 18x

(a)

117.

Factor. Do not type spaces.

$x^3-9x$

(a)

118.

Factor. Do not type spaces.

$x^3+9x$

119.

Factor. Do not type spaces.
$4x^2+24x-64$

(a)

120.

Factor. Do not type spaces
$3x^2+6x-105$

(a)

121.

Factor.
$3x^2+60x-30$

a)

$3\left(x-10\right)\left(x+1\right)$

b)

$3\left(x+2\right)\left(x-5\right)$

c)

$3\left(x-2\right)\left(x+5\right)$

d)

Not factorable

e)

$3\left(x^2+20x-10\right)$

122.

Factor.
$5x^2-5x-100$

a)

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

b)

$5\left(x^2-x-20\right)$

c)

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

d)

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

e)

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

123.

Factor.
$2x^2-42x+40$

a)

$2\left(x-1\right)\left(x-20\right)$

b)

$2\left(x^2-21x+20\right)$

c)

$\left(x-1\right)\left(x-20\right)$

d)

$2\left(x+1\right)\left(x+20\right)$

e)

$\left(x+1\right)\left(x+20\right)$

124.

Match each polynomial to its factored form:

a)

$x^2+5x+4$

1.

(x+4)(x+1)

b)

$x^2-5x+4$

2.

(x-4)(x-1)

c)

$x^2+3x-4$

3.

(x+4)(x-1)

d)

$x^2-3x-4$

4.

(x-4)(x+1)

e)

$10x^2-30x-40$

5.

$10\left(x-4\right)\left(x+1\right)$

125.

Factor
$x^7-6x^5+8$

a)

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

b)

$x\left(x^6-6x^4-8\right)$

c)

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

d)

$8\left(x^7-6x^{5\ }+1\right)$

e)

Not factorable

126.

Factor
$4x^2-16$

a)

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

b)

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

c)

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

d)

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

e)

Not factorable

127.

Factor
$9x^2+16$

a)

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

b)

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

c)

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

d)

$\left(3x+16\right)\left(3x-16\right)$

e)

Not factorable

128.

Factor

$3x^2-21x+30$

Do not type spaces

(a)

129.

Factor

$x^3+2x^2-15x$

Do not type spaces

(a)

130.

Factor

$2x^3+34x^2+32x$

Do not type spaces

(a)

131.

Factor

$72x^3-50x$

Do not type spaces

(a)

132.

Factor

$810x^2-640$

Do not type spaces

(a)

133.

Factor

$49x^3-16x$

Do not type spaces

(a)

134.

Factor

$49x^3+16x$

Do not type spaces

135.

Factor

$9x^3-15x$

136.

Factor

$4x^3+80x^2+48x$

137.

Match the following

a)

$16x^2+9$

1.

Not factorable

b)

$16x^2-9$

2.

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

c)

$16x^3-9x$

3.

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

d)

$32x^2-18$

4.

$2\left(4x+3\right)\left(4x-3\right)$

e)

$160x^7-90x^5$

5.

$10x^5\left(4x+3\right)\left(4x-3\right)$

138.

Simplify. Write in standard form.

$\left(x+3\right)^2+\left(x+4\right)$

139.

Simplify. Write in standard form.

$\left(x+3\right)+\left(x+4\right)^2$

140.

Simplify. Write in standard form.

$-3\left(2x-5\right)^2-11$

141.

Simplify. Write in standard form.

$-3\left(2x-5\right)-11$

142.

Simplify. Write in standard form.

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

143.

Simplify. Write in standard form.

$\left(2x-5\right)+\left(3x-7\right)^2$

144.

Simplify. Write in standard form.

$5\left(2x+7\right)^2+10$

145.

Simplify. Write in standard form.

$5\left(2x+7\right)+10$

146.

Which expressions are equivalent to

$x^2-10x+16$

Select all that apply

a)

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

b)

$\left(x-5\right)^2-9$

c)

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

d)

$\left(x+4\right)^2-10x$

e)

$\left(x-5\right)^2-9-10x$

147.

Simplify

$\left(5x+3\right)\left(2x+7\right)$

148.

Simplify. Write in standard form.

$\left(5x+3\right)^2+\left(2x+7\right)$

149.

Simplify. Write in standard form.

$\left(5x+3\right)+\left(2x+7\right)^2$

150.

Factor

$18x^7-6x^5$

151.

Simplify. Write in standard form.

$3\left(5x-7\right)-2\left(6x-8\right)$

152.

Simplify. Write in standard form.

$3\left(5x-7\right)^2-2\left(6x-8\right)$

153.

Simplify. Write in standard form.

$3x\left(5x-7\right)-2\left(6x-8\right)$

154.

Simplify. Write in standard form.

$3x\left(5x-7\right)-2\left(6x-8\right)^2$

155.

Simplify. Write in standard form.

$\left(3x-5\right)^2+\left(11x^2-13x+4\right)$

156.

Simplify. Write in standard form.

$\left(3x-5\right)^2-\left(11x^2-13x+4\right)$

157.

Simplify. Write in standard form.

$5\left(7x-2\right)-9\left(6x-1\right)$

158.

Simplify. Write in standard form.

$5\left(7x-2\right)^2-9\left(6x-1\right)$

159.

Simplify. Write in standard form.

$5\left(7x-2\right)-9\left(6x-1\right)^2$

160.

Simplify. Write in standard form.

$\left(7x-2\right)^2-\left(3x^2-10x-6\right)$

161.

Simplify. Write in standard form.

$\left(7x-2\right)^2+\left(3x^2-10x-6\right)$

162.

Simplify. Write in standard form.

$\left(7x-2\right)-\left(3x^2-10x-6\right)$

U4 - Polynomial Operations (2025)

Total questions: 162

Worksheet time: 4hrs 22mins

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