Home
A Summary of Factoring Polynomials
Factoring The Difference of 2 Squares
Factoring Trinomials
Quadratic Expressions
Factoring Trinomials
The 7 Forms of Factoring
Factoring Trinomials
Finding The Greatest Common Factor (GCF)
Factoring Trinomials
Quadratic Expressions
Factoring simple expressions
Polynomials
Factoring Polynomials
Fractoring Polynomials
Other Math Resources
Factoring Polynomials
Polynomials
Finding the Greatest Common Factor (GCF)
Factoring Trinomials
Finding the Least Common Multiples
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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.