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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.

1 Answer

3 votes

Answer:


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

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