Question

The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer 1

`x +1 - (4)/(x^3 + 3x^2 + 8)`

Explanation:

`volume=base \: area * height`

`height=(volume)/(base \: area)`

`\mathrm{Solve \: by \: long \: division.}`

`h=((x^4 + 4x^3 + 3x^2 + 8x + 4))/((x^3 + 3x^2 + 8))`

`h=x + (x^3 + 3x^2 + 4)/(x^3 + 3x^2 + 8)`

`h=x +1 - (4)/(x^3 + 3x^2 + 8)`

Answer 2

`Height = x (x^3+3x^2+4)/(x^3+3x^2+8)`

Explanation:

`Volume = Base \ Area\ * Height`

`Height = (Volume)/(Base \ Area)`

Where
`Volume = x^4+4x^3+8x+4` and
`Area = x^3+3x^2+8`

Putting in the formula

`Height = (x^4 + 4x^3 + 3x^2 + 8x + 4)/(x^3 + 3x^2 + 8)`

Doing long division, we get

`Height = x + (x^3+3x^2+4)/(x^3+3x^2+8)`

`Height = x (x^3+3x^2+4)/(x^3+3x^2+8)`

This is the simplifies form and it can't be further simplified.