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” )
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