Factor out the greatest common factor
The first step in factoring a polynomial is to find the greatest common factor for the terms
of the polynomial. The greatest common factor (GCF) is the largest term that is a factor of all terms in the polynomial. For example, the greatest common factor for 8x +12 is 4, since 4 is the largest term that is a factor of (that is, divides into) both 8x and 12. Using the distributive property,
8x + 12 = 4(2x) + 4(3)
= 4(2x + 3).
As a check, multiply 4 and 2x + 3. The result should be 8x + 12. Using the distributive property this way is called factoring out the greatest common factor.