An open-top box is made from a 14-inch-by-32-inch piece of cardboard, as shown below. The volume of the box is represented by V(x) = x(14 - 2x)(32 - 2x), where x is the height of the box.

Question

a. Write the volume of the box as a polynomial function in standard form.
b. Find the volume of the box if the height is 2 inches.

Answer 1

(a) just expand the polynomial.
(b) v = 2(14-4)(32-4) = 672 in^3