Mathematics: 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.

A cardboard box in the shape of a rectangular prism - id12288483, isidrocastanonox22wl

charitysamuels

29.04.2021

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

Step-by-step 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

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