POLYNOMIALS

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

2. Remember: Monomials
are separated
+ or _____ signs.
−
by _____

3. But, what is a monomial?
A number or variable or product
of numbers and variables.
6
5x2
- y 2 z3
x
½xy

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

5. Classify the following:
x +x y z −z
5
5
3 6
3x – 8xy
2
a + 2ab + b
2
2
4abc
5x
2
2
3x – 8xy
2

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. x +x y z −z
5
5
3 6
3x + 5
2
y + y + 3x m
7
6
4
4
2

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. −5 x + x − 4 x − 2
3
2
−4 x − 5 x + x − 2
2
3
24 x y − 12 x y + 6 x
2
3
2
4
( of “y” )
−12x y +24x y +6x
3
2
2
−5 x + x − 4 x − 2
2
−2
3
4
+ x −5x −4x
2
3
24 x y − 12 x y + 6 x 24 x y − 12 x y + 6 x
2
3
2
4
2
3
2
4

10. 2x + 5 y − 8
2
20
−3 x + 8 y − 2
3
6

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

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

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

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

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

16. ( x − 6)( x + 3)
x
2
−3x −18
( x − 1)( x + 8)
x + 7x − 8
2
( x + 2)( x − 7)
2
x − 5 x − 14

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