ppt alg2 henrico module polynomials

1. Exponents and
Monomials

2. Monomial is an expression that is a
number, a variable, or a product of a
number and variables.
Constant is a monomial containing no
variables.
Coefficient is a numerical factor of a
monomial.
Degree is the sum of the exponents of a
monomial’s variables.
Power is the expression of the form xn.

3. Laws of Exponents
1
Negative Exponents: a −n
= n
a
1
a
−n =a n
m +n
Multiplying Powers: a g a = a
m
n

4. Laws of Exponents
m
a m −n
Dividing Powers: n =a
a
Power of a Power: (a ) =a
m n mn
( ab )
m
Power of a Product: =a b m m

5. Laws of Exponents
n n
a a
Power of a Quotient:   = n
 b b
−n n
b a
  = bn
a
Power of Zero: a = 1
0

6. Examples using the laws of exponents:
1. (2ab )(−3a b c ) = −6a b c
2 4 2 5 4
2. (6x y2 3
)(−xyz ) = −6x y z
3 4
12
x
3. 4 = x 8
x

7. −10x y 2 4
4. 4 = −2x
5xy
5. (x )= x
2 4
8
6. (−2a b ) = 16a
3 2 4
12 8
b

8. 2
 3x y 
3 n
7.  5 3n 2 
x y z 
2
 3  9
=  2 2n 2  = 4 4n 4
x y z  x y z

9. −3 3 3
 4  n n
8.   = =
 4  64
n
−3 −3
 3x y   x 
3b 2b
9.  b 3 =  2
 −6x y   −2y 
2 3
 −2y  −8y 6
=  2b  = 6b
 x  x