Question

A cookie company packages its cookies in rectangular prism boxes designed with square bases that have both a length and width of 4 inches less than the height of the box. Write a polynomial that represents the volume of a box with height x inches.

Answer 1

h³- 8h² + 16h

Explanation:

The problem tells us that the length and width of these boxes are both 4 inches less than the height of the box.

So if we name h the height of the box, the width of the box would be h - 4 and the height of the box would be h - 4.

Now, the volume of a rectangular prism is given by V = height x width x length

So, considering the values we have in this problem we get:

V= height x width x volume

V = h (h-4)(h-4)

V= h(h-4)²

V= h (h²-8h + 16)

V = h³- 8h² + 16h

Therefore, the polynomial representing the volume of this box in terms of the height is h³- 8h² + 16h