Before using the other methods for factoring, this is the first type of factoring you should try. Basically, you’re reversing the distributive property. What you’re doing is finding the greatest common factor for all of the terms.
Examples:
Factor 2x + 4
Greatest common factor for both of the terms is 2.
2x + 4 = 2(x + 2)
Factor 4x2 + 12
Greatest common factor for both terms is 4.
4x2 + 12 = 4(x2 + 3)
Factor 5x2 + 10x + 25
Greatest common factor for all of the terms is 5.
5x2 + 10x + 25 = 5(x2 + 2x + 5)
Find the greatest common factor for 12, 3 and -9.
After playing with the numbers around, I got 3.
3(4x + y - 3)
So, 3(4x + y - 3) is the answer.