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Addition and Subtraction of Polynomials Worksheet

Addition and Subtraction of Polynomials Worksheet
  • Page 1
 1.  
Subtract the polynomial 7y - 4y2 - 6 from 2y + 3 - y2.
a.
3y2 - 5y + 9
b.
- 3y2 + 5y + 9
c.
5y2 - 9y + 9
d.
3y2 + 5y - 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.


Correct answer : (1)
 2.  
What is the sum of the polynomials 5y2 + y - 6 and 6y2 - 5y + 9?
a.
11y2 + 4y + 3
b.
12y2 - 4y + 5
c.
11y2 - 4y + 3
d.
13y2 - 4y + 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.]


Correct answer : (3)
 3.  
Subtract the polynomial 24y2 from 31y2.
a.
4y2
b.
55y2
c.
7y2
d.
-7y2


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.]


Correct answer : (3)
 4.  
Add the polynomials 3a + 11c and 9b - 8c and get the simplified value.
a.
3a + 9b + 3c
b.
3a + 8b - 3c
c.
3a + 9b - 3c
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.]


Correct answer : (1)
 5.  
Find the sum of the polynomials 2y2 + 7y and 4y2 - 2y.
a.
2y2 - y
b.
6y2 - 5y
c.
6y2 + 5y
d.
y2 - 5y


Solution:

2y2 + 7y + 4y2 - 2y
[Add]

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

= 6y2 + 5y
[Simplify.]


Correct answer : (3)
 6.  
Subtract the polynomial 5y2 + 1 from 2y2 + 2.
a.
-3y2 + 1
b.
2y2 - 1
c.
2y2 + 1
d.
-2y2 - 1


Solution:

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

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

= -3y2 + 1
[Simplify.]


Correct answer : (1)
 7.  
What is the sum of the polynomials 4y3 + 4y2 + 5y and 3y2 + 3 ?
a.
y3 - y2 - 5y - 3
b.
4y3 - 4y2 - 5y + 3
c.
4y3 + 7y2 + 5y + 3
d.
None of the above


Solution:

4y3 + 4y2 + 5y + 3y2 + 3
[Add the polynomials]

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

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


Correct answer : (3)
 8.  
What is the value of (5y2 + 1) - (-2y3 + 10y2 - 3)?
a.
y3 - 5y2 - 4
b.
2y3 + 5y2 + 1
c.
2y3 - 5y2 + 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]


Correct answer : (3)
 9.  
What is the simplified form of the polynomial obtained by subtracting -5x + 5y - 3z from 4x + 5y - 4z?
a.
9x + z
b.
x - y - 4z
c.
9x - 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]


Correct answer : (3)
 10.  
The degree of the polynomial 7y4 - 10y 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.


Correct answer : (3)

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