Question

The length of a rectangular prism is 4 more than 3 times the width, w. The volume of the prism is 3w^3 + 16w^2 + 16w. What is a simplified expression for the height of the prism?

Answer 1

Height = w + 4

Explanation:

3w³ + 16w² + 16w = w (3w² + 16w + 16)

= w (3w + 4) (w + 4)

The length of a rectangular prism is 4 more than 3 times the width, w

L = 3w + 4

R prism volume = L x W x H

Height = w + 4