3x5+3x4-18x3+18x2
The coefficients are 3,3,-18, and 18.  3 is the largest integer that
all of them are divisible by:

The variable parts are x5, x4, x3, and x2.  x2 is the largest
power that all of them will divide into. [It sounds contradictory
that "the smallest is the largest" but the smallest power is the
largest power that can be taken out]. 

So the greatest common factor GCF is 3x2, and

3x2(x3+x2-6x+6)

is the simplest factored form.


Edwin