Geometry Holly can make an open-topped box
out of a square piece of cardboard by cutting 3-inch
squares from the corners and folding up the sides
to meet. The volume of the resulting box is
V = 3x^2– 36x + 108, where x is the original
length and width of the cardboard.

a. Factor the polynomial expression from the volume
equation.

b. What is the volume of the box if the original length
of each side of the cardboard was 14 inches?

c. What is the original side length of the cardboard
when the volume of the box is 27 in^3?