Free Printable Polynomial Operations

1.

Add to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

2.

Find the sum.
(3 - 2x + 2x²) + (4x - 5 + 3x²)

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

3.

What is the type of polynomial 3x⁴ + 2x² + 5x ?

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

4.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

5.

Combine like terms to simplify:
(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

6.

What is the degree of the polynomial 3x⁴ + 2x² + 5x ?

a)

1

b)

2

c)

3

d)

4

7.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

8.

What is the perimeter of the triangle shown?

a)

9r²+r-5

b)

9r⁴+r²-4

c)

9r²-r+4

d)

9r²+r-4

9.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

10.

Add or Subtract to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

11.

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

12.

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

13.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

14.

What is the standard form of the polynomial,
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

15.

How many terms are in the following polynomial?
7x - 125 - 6x³+ 14x²

a)

-125

b)

2

c)

3

d)

4

16.

(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

17.

(3 - 2x + 2x²) + (4x - 5 + 3x²)

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

18.

(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

19.

(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

20.

What is the perimeter of the triangle shown?

***Perimeter is the SUM of ALL sides!***

a)

9r²+ r - 5

b)

9r⁴+ r²- 4

c)

9r²- r + 4

d)

9r²+ r - 4

21.

What is the perimeter of the rectangle?

**Perimeter is the SUM of ALL sides!***

a)

x² + 8x - 5

b)

2x² + 16x - 10

c)

2x² + 10x - 8

d)

6x - 2

22.

(4x²+ x) - (x²+ 2x)

a)

3x²- x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

23.

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

24.

(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

25.

(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

26.

Identify the degree of the monomial:
8a³

a)

8

b)

1

c)

3

d)

11

27.

A polynomial that has two terms is a:

a)

polynomial

b)

monomial

c)

binomial

28.

Classify the polynomial by its degree.
x² + 2x³ - 4

a)

A
binomial

b)

B
trinomial

c)

C
quadratic

d)

D
cubic

29.

Classify the polynomial by its number of terms.
4x² - 2

a)

A
monomial

b)

B
binomial

c)

C
trinomial

d)

D
polynomial

30.

Which is an example of a cubic monomial?

a)

A
x³ + 5

b)

B
x² + 3

c)

C
x² + 5x - 6

d)

D
5x³

31.

4x² + 8x - 7
is classified as a...

a)

Third Degree Monomial

b)

Second Degree Binomial

c)

Second Degree Trinomial

d)

Third Degree Cubic

32.

What is this expression classified as? $10x^5$

a)

5th degree Monomial

b)

10th degree Monomial

c)

5th degree Trinomial

d)

10th degree Polynomial

33.

Which of these is in Standard Form?

a)

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

b)

$5-3x$

c)

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

d)

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

34.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

35.

Name and Classify the Polynomial:
x² − 4

a)

quadratic binomial

b)

quadratic monomial

c)

linear binomial

d)

linear monomial

36.

Determine the leading coefficient of the following polynomial:

-8x - x³ +7x - 2

a)

-8

b)

-1

c)

7

d)

-2

37.

Which of the following polynomials is written in standard form?

a)

9 + 8x - 2x²

b)

10x + x³ - 4x² - 11

c)

x⁴ + 5x³ - 6x +1

d)

4x³+ 3x⁴ + 2x + 1

38.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

39.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

40.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

41.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

42.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

43.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

44.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

45.

Subtract the polynomials.
(3x³ + 3x² + 5) – (x³ – 2x² + x – 4)

a)

4x³ + 5x² + 9

b)

2x³ + 5x² – x + 9

c)

2x³ + 1x – 1x² – 1

d)

2x⁶ +5x⁵ – 1x – 1

46.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

47.

(3x − 6)(7x + 7)

a)

21x² − 63x + 42

b)

21x² − 21x − 42

c)

21x² − 42

d)

21x² + 63x + 42

48.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

49.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

50.

Simplify the expression
(x - 3)²

a)

x² - 6x + 9

b)

x² + 9

c)

x² + 6x - 9

d)

x² + 6x + 9

51.

Subtract the following polynomials
$\left(6x^2-3x+2\right)-\left(-4x^2+3x-6\right)$

a)

$2x^2-4$

b)

$10x^2-6x+8$

c)

$10x^2+8$

d)

$2x^2-6x-4$

52.

Multiply the following polynomials $\left(3x-2\right)\left(x^2+x-1\right)$

a)

$3x^3+x^2-5x+2$

b)

$3x^3+5x^2+5x-2$

c)

$3x^3+x^2-5x-2$

d)

$3x^3+5x^2+5x+2$

53.

Multiply the following polynomials
$\left(3x^2+3\right)\left(x+4\right)^2$

a)

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

b)

$3x^4+15x^2+12$

c)

$3x^4+24x^3+51x^2+24x+48$

d)

$3x^4-45x^2-48$

54.

Add the following polynomials $\left(3x-2x^2+3x^3-2\right)+\left(3x^2-2x-9\right)$

a)

$3x^3+x^2+5x+7$

b)

$3x^3-x^2+x-11$

c)

$3x^3+x^2+x-11$

d)

$3x^3+x^2-x-7$

55.

Simplify the expression.
2x(-2x - 3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

56.

Add the polynomials (x-2) and (x²+3)

a)

x²+x+1

b)

x³+5

c)

x³+1

d)

x³-1

57.

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

a)

2x² + x + 2

b)

x + 2

c)

2x² + x - 10

d)

x - 10

58.

Add or Subtract to Simplify:
(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

59.

How many terms are in the following polynomial?
3x³ - 2y + 8x -16

a)

1

b)

2

c)

4

d)

-16

60.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

d)

r ² + 7r + 49

61.

What is the degree of the polynomial:
7x³ – 8x² + 9

a)

5

b)

2

c)

6

d)

3

62.

The side length of a square is (x - 7), which of the following below would represent the area?

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

63.

a)

x+7

b)

x+2

c)

X-10

d)

X-7

64.

a)

x+7

b)

y+7

c)

Y-2

d)

2y-q

65.

a)

x+1

b)

13

c)

2x-1

d)

x²+1

66.

a)

x+1

b)

x+8

c)

x-9

d)

2x+1

67.

a)

4x

b)

21

c)

2x-1

d)

10x

68.

a)

2x - 5

b)

x - 4

c)

x + 4

d)

2x + 4

Polynomial Operations

Total questions: 68

Worksheet time: 5hrs 2mins

Similar Resources on Wayground