Finding the Greatest Common Factor (GFC)
After studying this lesson, you will be able to:
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 lesson will concentrate on the first step of factoring:
Factoring out the GCF.
Example 1
Factor 10y^{ 2} + 15y
We look for the GCF...it will be 5y
Here's how we factor: write the GCF 5y and then put
parentheses: 5y
Factoring is the same as dividing, so we divide each term by
5y and we put the result in the parentheses.
10y^{ 2} divided by 5y is 2y and 15y divided by 5y is
3: 5y ( 2y + 3 ) this is the answer
We can check the answer by multiplying 5y ( 2y + 3)
Distributing we will get 10y^{ 2} + 15y (which matches
the original problem)
Example 2
Factor 21ab^{ 2 } 33 a^{ 2} bc
We look for the GCF......it will be 3ab
Here's how we factor: write the GCF 3ab and then put
parentheses: 3ab
Factoring is the same as dividing, so we divide each term by
3ab and we put the result in the parentheses.
21ab^{ 2} divided by 3ab is 7b and  33 a^{ 2}
bc divided by 3ab is 11ac: 3ab ( 7b  11ac ) this is the answer
We can check the answer by multiplying : 3ab ( 7b  11ac )
Distributing we will get 21ab^{ 2 } 33 a^{ 2}
bc (which matches the original problem)
Example 3
Factor 6x^{ 3 }y^{ 2} + 14x^{ 2 }y + 2x^{
2 }
We look for the GCF......it will be 2x^{ 2 }
Here's how we factor: write the GCF 2x^{ 2 }and then
put parentheses: 2x^{ 2 }
Factoring is the same as dividing, so we divide each term by 2x^{
2 }and we put the result in the parentheses.
6x^{ 3 }y^{ 2} divided by 2x^{ 2} is
3xy^{ 2} and 14x^{ 2 }y divided by 2x^{ 2 }is
7y and 2x^{ 2 }divided by 2x^{ 2 }is 1
2x^{ 2}(3xy^{ 2 }+ 7 y + 1) this is the answer
We can check the answer by multiplying : 2x^{ 2}(3xy^{
2 }+ 7 y + 1)
Distributing we will get 6x^{ 3 }y^{ 2} + 14x^{
2 }y + 2x^{ 2 }(which matches the original problem)
