Adding Polynomials-Algebra1-Solved Examples

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

Solutions

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

Solutions

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

Solutions

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

Solutions

Step: 1

4y³ + 5y² + 5y + 3y² + 1

[Add the polynomials.]

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

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