Factoring Out the Opposite of the GCF
The GCF, the greatest common factor, for 6x^{2}  4x is 2x, but we can factor out
either 2x or its opposite, 2x:
6x^{2}  4x 
= 2x( 3x  2) 

= 2x(3x + 2) 
Example 1
Factoring out the opposite of the GCF
Factor out the GCF, then factor out the opposite of the GCF.
a) 5x  5y
b) x^{2}  3
c) x^{3} + 3x^{2}  5x
Solution
a) 5x  5y 
= 5(x  y) 
Factor out 5. 

= 5 (x + y) 
Factor out 5. 
b) x^{2}  3 
= 1(x^{2}  3) 
The GCF is 1. 

= 1(x^{2} + 3) 
Factor out 1. 
c) x^{3} + 3x^{2}  5x 
= x(x^{2} + 3x  5) 
Factor out x. 

= x(x^{2}  3x + 5) 
Factor out x. 
