GREATEST COMMON FACTOR: Example 1

Factor: 

     
  This expression  has two terms. The variable x is a common factor in both terms. 


 

 
x can be divided out of each term

The common factor  x is "undistributed" and placed to the left of a set of parentheses. The remaining factors are  placed inside the parentheses. 

Factoring Summary         Example 2       Example 3 

 

 

 

 

 

 

 

 

 


GREATEST COMMON FACTOR: Example 2

Factor: 

      
  This expression  has three terms. Each term has a common factor of 3 x2 y.  

HINT:
For variables containing exponents, look for the smallest exponent that appears in any one term. For example the first term has x4, the second term has x3 and the third term has x2. x2 will be a common factor.

 
3 x2 y can be divided out of each term. 

But what happens to the last term? All the factors are divided out, therefore 1 is left.


Check the remaining factor to be sure there is no common factor. If there is, then you did not extract the GREATEST common factor to begin with. 




no common factor                                             


          

 
    

 

 
     

Factoring Summary         Example 1       Example 3 

 

 

 

 

 

 

 

 

 

 


GREATEST COMMON FACTOR: Example 3

Factor: 

    
  This expression  has three terms. There is no common factor shared by ALL three terms. There is no GCF. Furthermore, the expression cannot be factored.

NOTE:
Always check for a common factor. If you cannot find one, look for other factoring patterns. If no other factoring patterns apply then you can conclude that the expression cannot be factored. Such and expression is called PRIME.
   

 

 

  

Factoring Summary         Example 1       Example 2