Question

A cardboard box in the shape of a rectangular prism has the dimensions shown. Write a polynomial in standard form to represent the volume of the box.

Answer 1

`Volume = x^3 +3x^2 -16x +12`

Explanation:

Given [missing from the question].

The dimensions are:

Length =(x + 6), Width = (x - 2) and Height = (x -1)

Required

Represent the volume as a polynomial

Volume is calculated as:

`Volume = Length * Width * Height`

So:

`Volume = (x + 6) * (x - 2) * (x - 1)`

Expand

`Volume = (x + 6) * (x^2 -2x -x +2)`

`Volume = (x + 6) * (x^2 -3x +2)`

Expand

`Volume = x^3 -3x^2 +2x +6x^2-18x +12`

Collect like terms

`Volume = x^3 -3x^2+6x^2 +2x -18x +12`

`Volume = x^3 +3x^2 -16x +12`