This document provides examples and instructions for dividing monomials and polynomials by monomials. It begins with an essential question about dividing monomials and polynomials by monomials. It then provides the quotient rule for exponents and two examples of simplifying expressions by dividing monomials. The examples show dividing terms with the same bases and subtracting the exponents. It concludes by providing a homework assignment of problems dividing multiples of 3.

1. SECTION 9-3
Divide by a Monomial

2. ESSENTIAL QUESTION
How do you divide monomials and polynomials by
monomials?
Where you’ll see this:
Landscaping, retail, interior design, geography, modeling

3. QUOTIENT RULE FOR
EXPONENTS
m
a m−n
n
=a
a
Same bases, subtract exponents

4. EXAMPLE 1
Simplify.
2 4 5
14y 9vw 80x y
a. b. c. 2 2
7y 15v 20x y

5. EXAMPLE 1
Simplify.
2 4 5
14y 9vw 80x y
a. b. c. 2 2
7y 15v 20x y
2y

6. EXAMPLE 1
Simplify.
2 4 5
14y 9vw 80x y
a. b. c. 2 2
7y 15v 20x y
3w
2y
5

7. EXAMPLE 1
Simplify.
2 4 5
14y 9vw 80x y
a. b. c. 2 2
7y 15v 20x y
3w
2y 2
4x y 3
5

8. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3

9. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3

10. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
2
2x
2x

11. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
2
2x
2x

12. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
2
2x 4x
−
2x 2x

13. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
2
2x 4x
−
2x 2x
x −2

14. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
4 2
2x2
4x 45t 30t 15t
− − +
2x 2x 3 3 3
x −2

15. EXAMPLE 2
Simplify.
4 2
2
2x − 4x 45t − 30t + 15t
a. b.
2x 3
4 2
2x2
4x 45t 30t 15t
− − +
2x 2x 3 3 3
x −2 4 2
15t − 10t + 5t

16. HOMEWORK

17. HOMEWORK
p. 388 #1-48 multiples of 3
“There is no expedient to which a man will not go to avoid the
labor of thinking.” - Thomas A. Edison