Rewrite the polynomial 6x4 − 24x3 + 72x2 by factoring out the gcf

The trick here is to recognize one or more factors common to each term.  For example,  6x4 − 24x3 + 72x2 = x^2(6x^2 - 24x + 72), so x^2 is one common factor.  Looking at (6x^2 - 24x + 72), you can easily see that 6 is a common factor, so now we have (6)(x^2)(x^2 - 4x + 12).  These last 3 terms do not have a common factor, so the factoring process stops here:

(6)(x^2)(x^2 - 4x + 12)