The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 inches and the height. A. Write a polynomial that represents the volume of the box in terms of its height (in inches). B. The volume of the box is 180 cubic inches.

or

Step-by-step explanation:

Let:

Given

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

Expand

Open brackets

Rewrite as:

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in:

Rewrite as:

Factorize:

Express as difference of two squares

This gives:

Since the height can not be negative, then H = 5 or H = 6

Recall that:

When H = 5

When H = 6

Hence, the dimensions of the box are:

or