Adding and Subtracting Polynomials
Monomial: a number, variable, or product of a number and variable.
Binomial: The sum or difference of two monomials.
Trinomials: The sum of difference of three monomials
Polynomial: A monomial or sum of monomials.
Degree of Monomial: The sum of the exponents on its variables.
Degree of Polynomial: The greatest degree of its monomials.
Polynomials are normally written in descending order.
Example: x 3  5x 2 1. The exponents go 3, 2, 0 so it is in descending order.
Leading Coefficient The coefficient of the largest number in the polynomial. In the
example, 1 is the leading coefficient because of x 3 .
Like Terms:
Same variable, same exponent.

Identifying if something is a monomial.
Monomial
10
3x
1
ab
2
1.8m 5
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

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Degree
0
1
1+2=3
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Not a Monomial
5+x
Reason
A sum is not a
monomial
2
A monomial
cannot have a
n
variable in the
5
denominator
a
A monomial
4

cannot have a
variable exponent
1
The variable must
x

have a whole
number exponent.
Example: Identifying and Classifying Polynomials: Tell whether the expression is a

polynomial. If it is a polynomial, find its degree and classify it by the number of its
terms. Otherwise, tell why it is not a polynomial.
Expression
Is a Polynomial?
9
2x 2  x  5
6n 4  8 n
n 2  3
7bc 3  4b 4 c
Yes
Yes
No; Variable Exponent
No; Negative Exponent
Yes
Classify by Degree and
Number of Terms
0 degree monomial
2nd degree trinomial
5th degree binomial
Adding Polynomials
To add polynomials, add like terms. You can us a vertical or horizontal
format.
Example: Add Polynomials
Find the Sum
a) Solve using vertical format:
2x 3  5x 2  x 2x 2  x 3 1
Solution: Align like terms in vertical columns and add.
2x 3  5x 2  x
+ x 3  2x 2
-1
3
2
3x  3x  x 1
b) Solve using horizontal format:

3x 2 
x  6  x 2  4x 10


 

Solution:
 Group Like Terms and Simplify
2
3x  x  6 x 2  4 x  10 3x 2  x 2  x  4 x   6  10

 4 x 2  5x  4
Try This:
3
2
3
 Find the sum: 5x  4x  2x 4x  3x  6
Subtracting Polynomials
 To subtract a polynomial, add its opposite. To find the opposite of a
polynomial, multiply each of its terms by -1.
Example: Subtract Polynomials
Find the Difference
a) Solve using the vertical format:
4n 2  5 2n 2  2n  4
Solution:
4n
+5
- 2n 2  2n  4
2




b) Solve using the horizontal format:
2
2
4x  3x  5 3x  x  8 

4n 2
+5
+ 2n 2  2n  4
6n 2  2n  9
Solution:

2
2
4
x

3x

5

3x

x

8


 
 4 x 2  3x  5  3x 2  x  8
 4 x 2  3x 2  3x  x   5  8

 x 2  2x  13
Try This: 4x 2  7x  5x 2  4x  9
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