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 Number of inequalities to solve: 23456789
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After studying this lesson, you will be able to:

• Factor various types of problems.

Steps of Factoring:

1. Factor out the GCF

2. Look at the number of terms:

• 2 Terms: Look for the Difference of 2 Squares
• 3 Terms: Factor the Trinomial
• 4 Terms: Factor by Grouping

3. Factor Completely

4. Check by Multiplying

This section is a review of the types of factoring we'vecovered so far. Follow the steps listed above to factor theproblems.

Example 1

Factor 3x 2 - 27

1 st : Look for a GCF....the GCF is 3 so we factorout 3: 3( x 2 - 9)

2 nd : Look at the number of terms in theparenthesis. There are 2 terms and it is the difference of 2squares. We factor the difference of 2 squares (keeping the 3).3(x + 3) ( x - 3)

3 rd : Now, make sure the problem is factoredcompletely. It is.

4 th : Check by multiplying.

Example 2

Factor 9y 2 - 42y + 49

1 st : Look for a GCF....the GCF is 1 so we don'thave to worry about that.

2 nd : Look at the number of terms. There are 3terms so we factor the trinomial.

-make 2 parentheses

-using the sign rules, we know the signs will be the samebecause the constant term is positive

- we also know they will be negative because theinside/outside combination must equal -58y

-find the factors of the 1 st term: 1y, 9y and 3y, 3y . Let'stry 3y, 3y

-find the factors of the constant term: 1, 49 and 7, 7. Let'stry 7, 7 (3y - 7) (3y - 7)

-check the inside/outside combination: inside we have -21y andoutside we have -21y which adds up to -42y

3 rd : Now, make sure the problem is factoredcompletely. It is.

4 th : Check by multiplying.

Example 3

Factor x 3 - 5x 2 - 9x + 45

1 st : Look for a GCF....the GCF is 1 so we don'thave to worry about that.

2 nd : Look at the number of terms. There are 4terms so we factor by grouping.

Group the terms (x 3 - 5x 2 ) + (- 9x +45 )

Take the GCF of the each group: x 2 (x -5 )(- 9(x - 5 ))

Take the GCF of the entire problem: (x - 5 )(x2 -9)

3 rd : Now, make sure the problem is factoredcompletely. It isn't. We can factor the second parenthesis.

(x - 5 )(x + 3)(x - 3)

4 th : Check by multiplying.