﻿ Addition and Subtraction of Polynomials Worksheet | Problems & Solutions

# Addition and Subtraction of Polynomials Worksheet

Addition and Subtraction of Polynomials Worksheet
• Page 1
1.
Subtract the polynomial 7$y$ - 4$y$2 - 6 from 2$y$ + 3 - $y$2.
 a. 3$y$2 - 5$y$ + 9 b. - 3$y$2 + 5$y$ + 9 c. 5$y$2 - 9$y$ + 9 d. 3$y$2 + 5$y$ - 3

#### Solution:

7y - 4y2 - 6 , 2y + 3 - y2
[Original Polynomials.]

- 4y2 + 7y - 6 , - y2 + 2y + 3
[Write each expression in standard form.]

- y2 + 2y + 3
(-) - 4y2 + 7y - 6
.................................
3y2 - 5y + 9
.................................
[Line up like terms vertically and subtract.]

The result is 3y2 - 5y + 9.

2.
What is the sum of the polynomials 5$y$2 + $y$ - 6 and 6$y$2 - 5$y$ + 9?
 a. 11$y$2 + 4$y$ + 3 b. 12$y$2 - 4$y$ + 5 c. 11$y$2 - 4$y$ + 3 d. 13$y$2 - 4$y$ + 6

#### Solution:

(5y2 + y - 6) + (6y2 - 5y + 9)
[Write the expression for the sum of the polynomials.]

= (5y2 + 6y2) + (y - 5y) + (-6 + 9)
[Group like terms.]

= (5 + 6)y2 + (1 - 5)y + (-6 + 9)
[Use distributive property.]

= 11y2 - 4y + 3
[Simplify.]

3.
Subtract the polynomial 24$y$2 from 31$y$2.
 a. 4$y$2 b. 55$y$2 c. 7$y$2 d. -7$y$2

#### Solution:

31y2 - 24y2
[Subtraction of the polynomials using horizontal format.]

= (31 - 24)y2
[Use distributive property.]

= 7y2
[As the exponents are same, subtract the coefficients.]

4.
Add the polynomials 3$a$ + 11$c$ and 9$b$ - 8$c$ and get the simplified value.
 a. 3$a$ + 9$b$ + 3$c$ b. 3$a$ + 8$b$ - 3$c$ c. 3$a$ + 9$b$ - 3$c$ d. None of the above

#### Solution:

(3a + 11c) + (9b - 8c)
[Write the expression for adding the polynomials.]

= 3a + 9b + 11c - 8c
[Use Commutative and Associative properties of addition and to group like terms.]

= 3a + 9b + 3c
[Simplify the like terms.]

5.
Find the sum of the polynomials 2$y$2 + 7$y$ and 4$y$2 - 2$y$.
 a. 2$y$2 - $y$ b. 6$y$2 - 5$y$ c. 6$y$2 + 5$y$ d. $y$2 - 5$y$

#### Solution:

2y2 + 7y + 4y2 - 2y

= 2y2 + 4y2 + 7y - 2y
[Group like terms.]

= 6y2 + 5y
[Simplify.]

6.
Subtract the polynomial 5$y$2 + 1 from 2$y$2 + 2.
 a. -3$y$2 + 1 b. 2$y$2 - 1 c. 2$y$2 + 1 d. -2$y$2 - 1

#### Solution:

2y2 + 2 - (5y2 + 1)
[Subtract.]

= 2y2 -5y2 + (2 - 1)
[Group like terms]

= -3y2 + 1
[Simplify.]

7.
What is the sum of the polynomials 4$y$3 + 4$y$2 + 5$y$ and 3$y$2 + 3 ?
 a. $y$3 - $y$2 - 5$y$ - 3 b. 4$y$3 - 4$y$2 - 5$y$ + 3 c. 4$y$3 + 7$y$2 + 5$y$ + 3 d. None of the above

#### Solution:

4y3 + 4y2 + 5y + 3y2 + 3

= 4y3 + 4y2 + 3y2 + 5y + 3
[Group like terms]

= 4y3 + 7y2 + 5y + 3
[Combine like terms]

8.
What is the value of (5$y$2 + 1) - (-2$y$3 + 10$y$2 - 3)?
 a. $y$3 - 5$y$2 - 4 b. 2$y$3 + 5$y$2 + 1 c. 2$y$3 - 5$y$2 + 4 d. None of the above

#### Solution:

(5y2 + 1) - (-2y3 + 10y2 - 3)
[Original polynomial]

= 5y2 + 1 + 2y3 - 10y2 + 3
[Apply distributive property.]

= 2y3 + 5y2 - 10y2 + 1 + 3
[Group like terms]

= 2y3 - 5y2 + 4
[Combine like terms]

9.
What is the simplified form of the polynomial obtained by subtracting -5$x$ + 5$y$ - 3$z$ from 4$x$ + 5$y$ - 4$z$?
 a. 9$x$ + $z$ b. $x$ - $y$ - 4$z$ c. 9$x$ - $z$ d. $x$ + $y$ + $z$

#### Solution:

-5x + 5y - 3z and 4x + 5y - 4z
[Original polynomials]

4x + 5y - 4z - (-5x + 5y - 3z) = 4x + 5y - 4z + 5x - 5y + 3z
[Apply distributive property.]

= 4x + 5x + 5y - 5y - 4z + 3z
[Group like terms]

= 9x - z
[Combine like terms]

10.
The degree of the polynomial 7$y$4 - 10$y$ is _______.
 a. 6 b. 3 c. 4 d. 5

#### Solution:

7y4 - 10y
[Original Polynomial.]

The highest exponent of y will be the degree of the polynomial.

The highest exponent of y in the polynomial is 4.

The degree of the polynomial is 4.