This document introduces factoring expressions by defining terms, factors, and coefficients. It explains that factoring is rewriting an expression as a product of its factors. Examples are provided of factoring monomials, binomials, and trinomials by multiplication. Key terms discussed include monomial, binomial, trinomial. The next lesson will cover finding the factors of expressions.

1. 3 2
6x 3x 15x
Introduction to Factoring

2. 3 2
6x 3x 15x
The terms of an expression
are the parts of the
expression joined by addition
or subtraction

3. 3 2
6x 3x 15x
First term
3
6x

4. 3 2
6x 3x 15x
Second term
2
3x
Notice that we include the negative
sign as part of the term

5. 3 2
6x 3x 15x
Third term 15x

6. 3 2
6x 3x 15x
Each term of the expression
has one or more factors.
Factors are the parts of an
expression joined by
multiplication.

7. 3 2
6x 3x 15x
Factors of the first term
3
6x 3 2 x x x

8. 3 2
6x 3x 15x
Factors of the second term
2
3x 13 x x
Notice that we include negative one
as a factor of the term

9. 3 2
6x 3x 15x
Factors of the third term
15 x 3 5 x

10. 3 2
6x 3x 15x
When a factor is a number,
it is called a coefficient

11. 3 2
6x 3x 15x
Coefficient of the first term
6

12. 3 2
6x 3x 15x
Coefficient of the second term
3
Notice that we include the negative
sign as part of the coefficient

13. 3 2
6x 3x 15x
Coefficient of the third term
15

14. 3 2
6x 3x 15x
Given any expression,
you should be able to identify its
•Terms
•Factors
•Coefficients

15. 3 2
6x 3x 15x
Since factors are parts of an
expression joined by multiplication,
factoring is rewriting an expression
as a product

16. 3 2
6x 3x 15x
The expression above can be
factored as
2
3x 2 x x 5

17. 3 2
6x 3x 15x
You can check this by multiplying
with the distributive property
2
3x 2 x x 5
Combine 3x with the factors of each
term, rearrange the factors, and
simplify using the rules of exponents

18. 3 2
6x 3x 15x
2
3x 2 x x 5
2
3x 2 x 3x x 3x 5
3 2
6x 3x 15 x

19. We have not talked about how to
factor but here are some examples
Check these examples of factoring
by multiplication

20. Here we have factored a monomial
as the product of two other
monomials
2
6x 2x 3x
Multiply 2 x 3x to verify the
product 6x 2

21. Here we have factored out a common
factor of 2
2 2
4x 6x 8 2 2x 3x 4
Multiply 2 2 x 3 x 4 to verify the
2
product 4 x 6 x 8
2

22. Here we have factored a binomial as
a product of two other binomials
2
x 9 x 3 x 3
Multiply x 3 x 3 to verify the
product x 2 9

23. Here we have factored a trinomial as
a product of two binomials
2
x 7 x 10 x 2 x 5
Multiply x 2 x 5 to verify the
product x 2 7 x 10

24. Vocabulary Review:
The name of an expression is
determined by the number of its
terms
1. Monomial
2. Binomial
3. Trinomial

25. This expression is a monomial
2
6x
The expression has one term

26. This expression is a binomial
2
x 9
The expression has two terms

27. This expression is a trinomial
2
x 7 x 10
The expression has three terms
In the Next Lesson we will begin
learn how to find the factors of an
expression

28. Brought to you by the
Math Department of
Moreau Catholic High School
A Holy Cross School
Educating Hearts & Minds
27170 Mission Blvd
Hayward, CA 94544
www.moreaucatholic.org
Last Update 10/29/2011