Question

A box in the shape of a rectangular prism has a width that is 5 inches greater than the height and a length that is 2 inches greater than the width. Write a polynomial expression in standard form for the volume of the box. Explain the meaning of any variables used.

Answer 1

The volume of the rectangular prism can be express in standard polynomial as follows:

x³ + 12x² + 35x

How to find the volume of a rectangular prism?

volume of a rectangular prism = lwh

where

• l = length
• w = width
• h = height

Therefore,

let

height = x

width = x + 5

length = x + 5 + 2 = x + 7

Therefore,

volume = x(x + 5)(x + 7)

volume = x(x² + 7x + 5x + 35)

volume = x(x² + 12x + 35)

volume = x³ + 12x² + 35x

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