This document provides an overview of polynomials including: - Classifying polynomials by the number of terms they contain such as one term, two terms, etc. - Defining monomials as numbers, variables, or products of numbers and variables and the degree of monomials and polynomials. - Explaining how to order variables in ascending and descending order. - Covering how to add, subtract, and multiply polynomials including examples of each operation.

1. POLYNOMIALS REVIEW
Classifying Polynomials
Adding & Subtracting Polynomials
Multiplying Polynomials

2. Remember: Monomials
are separated
by _____ or _____ signs.
 

3. But, what is a monomial?
A number or variable or product
of numbers and variables.
5x2
6 x
- y2
z3 ½xy

4. “Poly” means _________________?
Polynomials can be classified
according to the number of
terms they have.
• ONE TERM –
• TWO TERMS –
• THREE TERMS -

5. 5 5 3 6 2
x x y z z
 
Classify the following:
3x2
– 8xy
4abc
3x2
– 8xy
5x2
a2
+ 2ab + b2

6. DEGREE………………
The degree of a monomial is
determined by adding the
exponents of its variables.
So, to find the degree of a
POLYnomial, find the degree of
each separate MONOmial. The
Monomial with the HIGHEST
sum determines the degree of
the problem.

7. 5 5 3 6 2
x x y z z
 
2
3 5
x 
7 6 4 4
3
y y x m
 

8. Ascending & Descending
Order
• Ascending – means to count up!
So, order the VARIABLES
exponents from least to greatest.
• Descending – means to count down!
So, order the VARIABLES
exponents from greatest to least.

9. 2 3
5 4 2
x x x
   
3 2
4 5 2
x x x
   
2 3 2 4
24 12 6
x y x y x
 
3 2
12x y
 2
24x y
 4
6x

2 3
5 4 2
x x x
    3
4x

2
 x
 2
5x

2 3 2 4
24 12 6
x y x y x
  2 3 2 4
24 12 6
x y x y x
 
( of “y” )

10. 2
2 5 8
x y
 
20
3
3 8 2
x y
  
6

11. Adding & Subtracting
Polynomials
2
(3 5 6)
y y
  2
(7 9)
y
 
2
10y 5y
 15

2 2
(3 3 )
a ab b
 
2
(4 6 )
ab b
 
2
3a 7ab
 2
5b

2
(3 2)
x  (9x
 1)

2
(7x
 4 )
x

2
10 5 1
x x
 

12. 2 2
(4 3 5 )
x y xy
  (8xy
 2
6x
 2
3 )
y

2 2
2 3 6
x xy y
  
Subtract
2
8 5
x x
   from
2
2 6
x x

2
3x 2x
 5

4
(8 6)
x  2
(4x
 2)
 4
(2x

2
)
x

4 2
10 5 8
x x
 

13. Multiplying Polynomials
3
4 (3 3 )
x x y

4
12 12
x xy
 4
5 (8 5 )
x x y
 
5
40x
 25

4
x y
4 3 2
3 (2 4 4 6)
x x x x
  
6 7
x 12
 6
x 12

5
x 18
 4
x

14. 2 2 3
6 ( 4 2 )
x y x xy y
  
4
6x y
 3 2
24x y

2 4
12x y

2 2 3
2 ( 4 7 )
x y x xy y
  
4
2x y
 3 2
8x y
 2 4
14x y

( 7)( 1)
x x
 
2
x 8x
 7

( 4)( 2)
x x
 
2
x 6x
 8


15. ( 6)( 5)
x x
 
2
x 11x
 30

( 7)( 3)
x x
 
2
x 10x
 21

( 9)( 3)
x x
 
2
x 6x
 27


16. ( 6)( 3)
x x
 
2
x 3x
 18

( 1)( 8)
x x
 
2
7 8
x x
 
( 2)( 7)
x x
 
2
5 14
x x
 

17. Tie Breaker
(3x + 2) (2x + 3)
6x2 + 13x + 6