ADDING POLYNOMIALS WORKSHEET

Problem 1 :

Add :

(2x + 3y) and (5x + 4y)

Problem 2 :

Add :

(2a - b), (3c - 2b) and (5a - 4c)

Problem 3 :

Add :

(5x2 + 2x - 7) and (6 - x - 4x2)

Problem 4 :

Add :

(3x3 - 2x2 - x + 4) and (2x3 + 7x2 - 3x - 3)

Problem 5 :

Add :

2(x3 - x2 + 6x - 2) and (5x6 + 7x5 - 3x - 3)

Problem 6 :

Add the following two polynomials. 

-1(x6 + x3 + 6x2 - 2) and 2(5x6 + 7x5 - 3x - 3)

Problem 7 :

Add :

5(5x6 + 2x3 - 6x2 - 2) + 6(-3x6 + 2x5 + 2x + 1)

Problem 8 :

Add :

5(x4 - x3 + 5) and  2(x4 - 5x2 - 7)

Problem 9 : 

Add :

3(6x4 - 2x3 - 3) and 2(2x4 - x2 - 8)

Problem 10 :

The profits of two different production plants can be modeled as shown below, where x' is the number of units produced at each plant. 

Eastern Plant : 

-0.03x2 + 26x - 1600

Western Plant : 

-0.02x2 + 20x - 1800

Use the information above to write a polynomial that represents the total profits from both plants. 

Detailed Answer Key

Problem 1 :

Add :

(2x + 3y) and (5x + 4y)

Solution : 

=  (2x + 3y) + (5x + 4y)

=  2x + 3y + 5x + 4y

Group like terms together. 

=  (2x + 5x) + (3y + 4y)

Combine like terms. 

=  7x + 7y

Problem 2 :

Add :

(2a - b), (3c - 2b) and (5a - 4c)

Solution : 

=  (2a - b) + (3c - 2b) + (5a - 4c)

=  2a - b + 3c - 2b + 5a - 4c

Group like terms together. 

=  (2a + 5a) + (-b + 2b) + (3c - 4c)

Combine like terms. 

=  7a + b - c

Problem 3 :

Add :

(5x2 + 2x - 7) and (6 - x - 4x2)

Solution : 

=  (5x2 + 2x - 7) + (6 - x - 4x2)

=  5x2 + 2x - 7 + 6 - x - 4x2

Group like terms together. 

=  (5x2 - 4x2) + (2x - x) + (-7 + 6)

Combine like terms. 

=  x2 + x - 1

Problem 4 :

Add :

(3x3 - 2x2 - x + 4) and (2x3 + 7x2 - 3x - 3)

Solution : 

=  (3x3 - 2x2 - x + 4) + (2x3 + 7x2 - 3x - 3)

Distributive Property.

=  3x3 - 2x2 - x + 4 + 2x3 + 7x2 - 3 x - 3

Group like terms together. 

=  (3x3 + 2x3) + (-2x2 + 7x2) + (-x - 3x) + (4 - 3)

Combine like terms. 

=  5x3 + 5x2 - 4x + 1 

Problem 5 :

Add :

2(x3 - x2 + 6x - 2) and (5x6 + 7x5 - 3x - 3)

Solution : 

=  2(x3 - x2 + 6x - 2) + (5x6 + 7x5 - 3x - 3)

Distributive Property.

=  2x3 - 2x2 + 12x - 4 + 5x6 + 7x5 - 3x - 3

Group like terms together. 

=  5x6 + 7x5 + 2x3 - 2x2 + (12x - 3x) + (-4 - 3)

Combine like terms. 

=  5x6 + 7x5 + 2x3 - 2x2 + 9x - 7

Problem 6 :

Add the following two polynomials. 

-1(x6 + x3 + 6x2 - 2) and 2(5x6 + 7x5 - 3x - 3)

Solution : 

=  -1(x6 + x3 + 6x2 - 2) + 2(5x6 + 7x5 - 3x - 3)

=  -x6 - x3 - 6x2 + 2 + 10x6 + 14x5 - 6x - 6

=  -x6 + 10x6 + 14x5 - x3 - 6x2 - 6x + 2 - 6

=  9x6 + 14x5 - x3 - 6x2 - 6x - 4

Problem 7 :

Add :

5(5x6 + 2x3 - 6x2 - 2) + 6(-3x6 + 2x5 + 2x + 1)

Solution : 

=  5(5x6 + 2x3 - 6x2 - 2) + 6(-3x6 + 2x5 + 2x + 1)

Distributive Property.

=  25x6 + 10x3 - 30x2 - 10 - 18x6 + 12x5 + 12x + 6

Group like terms together. 

=  (25x6 - 18x6) + 12x5 + 10x3 - 30x2 + 12x + (-10 + 6)

Combine like terms. 

=  7x6 + 12x5 + 10x3 - 30x2 + 12x - 4

Problem 8 :

Add :

5(x4 - x3 + 5) and  2(x4 - 5x2 - 7)

Solution :

=  5(x4 - x3 + 5) +  2(x4 - 5x2 - 7)

Distributive Property.

=  5x4 - 5x3 + 25 + 2x4 - 10x2 - 14

Group like terms together. 

=  (5x4 + 2x4) - 5x3 - 10x2 + (25 - 14)

Combine like terms. 

=  7x4 - 5x3 - 10x2 + 11

Problem 9 : 

Add :

3(6x4 - 2x3 - 3) and 2(2x4 - x2 - 8)

Solution : 

=  3(6x4 - 2x3 - 3) + 2(2x4 - x2 - 8)

Distributive Property.

=  18x4 - 6x3 - 9 + 4x4 - 2x2 - 16

Group like terms together. 

=  (18x4 + 4x4) - 6x3 - 2x2 + (-9 - 16)

Combine like terms. 

=  22x4 - 6x3 - 2x2 - 25

Problem 10 :

The profits of two different production plants can be modeled as shown below, where x' is the number of units produced at each plant. 

Eastern Plant : 

-0.03x2 + 26x - 1600

Western Plant : 

-0.02x2 + 20x - 1800

Use the information above to write a polynomial that represents the total profits from both plants. 

Solution :

Total profits from both plants :

=  Eastern plant profits + Western plant profits

=  (-0.03x2 + 26x - 1600) + (-0.02x2 + 20x - 1800)

=  -0.03x2 + 26x - 1600 - 0.02x2 + 20x - 1800

Group like terms together. 

=  (-0.03x2 - 0.02x2) + (26x + 20x) + (-1600 - 1800)

Combine like terms. 

=  -0.05x2 + 46x - 3400

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