**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 8*x *+12 is 4, since 4 is the largest term that is a factor of (that is, divides into) both 8*x *and 12. Using the distributive property,

8*x *+ 12 = **4**(2*x*) + **4**(3)

= **4**(2*x *+ 3).

As a check, multiply 4 and 2*x *+ 3. The result should be 8*x *+ 12. Using the distributive property this way is called *factoring out the greatest common factor*.