Solved Examples and Worksheet for Adding Polynomials

Q1Use a horizontal format to add: (5y2 + y - 10) + (5y2 - 5y + 13)
A. 10y2 + 4y - 3
B. 10y4 - 4y2 + 3
C. 10y2 + 6y + 23
D. 10y2 - 4y + 3

Step: 1
(5y2 + y - 10) + (5y2 - 5y + 13)
[Horizontal format.]
Step: 2
= 5y2 + y - 10 + 5y2 - 5y + 13
Step: 3
= 10y2 - 4y + 3
Correct Answer is :   10y2 - 4y + 3
Q2Add the polynomials 4b + 7y and 6z - 4y.

A. 4b + 7y + 6z - 4y
B. 4b + 6z - 3y
C. 4b + 6z + 3y
D. 10bz + 3y

Step: 1
(4b + 7y) + (6z - 4y)
[Write the expression for adding the polynomials.]
Step: 2
= 4b + 6z + 7y - 4y
[Use Commutative and Associative properties of addition and group like terms.]
Step: 3
= 4b + 6z + 3y
[Simplify like terms.]
Correct Answer is :   4b + 6z + 3y
Q3Find the sum of the polynomials 3y2 + 5y and 4y2 - 2y.

A. 7y2 - 3y
B. 7y2 + 3y
C. y2 - 3y
D. 2y2 - y

Step: 1
3y2 + 5y + 4y2 - 2y
[Write the expression for adding the polynomials.]
Step: 2
= 3y2 + 4y2 + 5y - 2y
[Group like terms.]
Step: 3
= 7y2 + 3y
[Simplify.]
Correct Answer is :   7y2 + 3y
Q4Find the sum of the polynomials 4y3 + 5y2 + 5y and 3y2 + 1.
A. 4y3 + 8y2 + 5y + 1
B. 8y4 + 4y3 + 5y + 1
C. 5y3 + 4y2 + 5y
D. 7y3 + 6y2 + 5y

Step: 1
4y3 + 5y2 + 5y + 3y2 + 1
Step: 2
= 4y3 + 5y2 + 3y2 + 5y + 1
[Group like terms.]
Step: 3
= 4y3 + 8y2 + 5y + 1
[Combine like terms.]
Correct Answer is :   4y3 + 8y2 + 5y + 1
Q5Add the two polynomials 3y3 - 3y2 + 7y - 4 and 6y + 4y2 - 7.

A. 3y3 + y2 + 13y + 11
B. 3y3 - y2 - 13y - 11
C. 3y3 + y2 + 13y - 11
D. 3y3 - y2 + 13y - 11

Step: 1
3y3 - 3y2 + 7y - 4, 6y + 4y2 - 7
[Original polynomials.]
Step: 2
3y3 - 3y2 + 7y - 4, 4y2 + 6y - 7
[Write each expression in standard form.]
Step: 3
3y3 - 3y2 + 7y - 4
(+)             4y2 + 6y - 7
.......................................
3y3 + y2 + 13y - 11
.......................................
[Line up like terms vertically and add like terms.]
Step: 4
The sum of the two polynomials is 3y3 + y2 + 13y - 11.
Correct Answer is :   3y3 + y2 + 13y - 11
Q6Add the two polynomials 6y3 - 3y2 + 8y - 7 and 9y + 4y2 - 6.

A. 6y3 + y2 + 17y - 13
B. 6y3 - y2 - 17y + 13
C. 6y3 - y2 + 17y - 13
D. 6y3 + y2 + 17y + 13

Step: 1
6y3 - 3y2 + 8y - 7, 9y + 4y2 - 6
[Original polynomials.]
Step: 2
6y3 - 3y2 + 8y - 7, 4y2 + 9y - 6
[Write each expression in standard form.]
Step: 3
6y3 - 3y2 + 8y - 7
(+)               4y2 + 9y - 6
......................................
6y3 + y2 + 17y - 13
......................................
[Line up like terms vertically and add like terms.]
Step: 4
The sum of the two polynomials is 6y3 + y2 + 17y - 13.
Correct Answer is :   6y3 + y2 + 17y - 13
Q7Add the two polynomials 5y + 3y2 - 4 and 6y + 1 - 6y2.

A. - 3y2 + 11y + 3
B. - 3y2 - 11y - 3
C. - 3y2 + 11y - 3
D. 3y2 + 11y - 3

Step: 1
5y + 3y2 - 4, 6y + 1 - 6y2
[Original Polynomials.]
Step: 2
The polynomials in the standard form are 3y2 + 5y - 4 and - 6y2 + 6y + 1
[Write each expression in the decreasing order of the exponents of variable y.]
Step: 3
3y2 + 5y - 4
(+)     - 6y2 + 6y + 1
.................................
- 3y2 + 11y - 3
.................................
[Line up like terms vertically and group like terms.]
Step: 4
The sum of the polynomials is - 3y2 + 11y - 3.
Correct Answer is :   - 3y2 + 11y - 3
Q8Add the two polynomials 7y3 + 3y2 - 8y + 4 and - 7 - 3y3 + 7y2 + 7y.

A. 4y3 + 10y2 + y - 3
B. 4y3 + 10y2 - y - 3
C. 4y3 - 10y2 - y - 3
D. 4y3 - 10y2 + y - 3

Step: 1
7y3 + 3y2 - 8y + 4, - 7 - 3y3 + 7y2 + 7y
[Original Polynomials.]
Step: 2
7y3 + 3y2 - 8y + 4, - 3y3 + 7y2 + 7y - 7
[Write each polynomial in standard form.]
Step: 3
7y3 + 3y2 - 8y + 4
(+)     - 3y3 + 7y2 + 7y - 7
........................................
4y3 + 10y2 - y - 3
........................................
[Line up like terms vertically and add like terms.]
Step: 4
The sum of the two polynomials is 4y3 + 10y2 - y - 3.
Correct Answer is :   4y3 + 10y2 - y - 3
Q9Add the two polynomials 7y3 + 4y2 - 6y + 5 and - 7 - 4y3 + 4y2 + 5y.
A. 3y3 - 8y2 - y - 2
B. 3y3 - 8y2 + y - 2
C. 3y3 + 8y2 - y - 2
D. 3y3 + 8y2 + y - 2

Step: 1
7y3 + 4y2 - 6y + 5, - 7 - 4y3 + 4y2 + 5y
[Original Polynomials.]
Step: 2
7y3 + 4y2 - 6y + 5, - 4y3 + 4y2 + 5y - 7
[Write each polynomial in standard form.]
Step: 3
7y3 + 4y2 - 6y + 5
(+)     - 4y3 + 4y2 + 5y - 7
...........................................
3y3 + 8y2 - y - 2
...........................................
[Line up like terms vertically and add like terms.]
Step: 4
The sum of the two polynomials is 3y3 + 8y2 - y - 2.
Correct Answer is :   3y3 + 8y2 - y - 2
Q10Use a horizontal format to add:
(5y2 + y - 9) + (4y2 - 5y + 12)

A. 9y2 + 6y + 21
B. 9y2 + 4y - 3
C. 9y4 - 4y2 + 3
D. 9y2 - 4y + 3

Step: 1
(5y2 + y - 9) + (4y2 - 5y + 12)
[Horizontal format.]
Step: 2
= 5y2 + 4y2 + y - 5y - 9 + 12
[Grouping like terms.]
Step: 3
= 9y2 - 4y + 3
[Simplify.]
Correct Answer is :   9y2 - 4y + 3