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

Answer:

$Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}$

Step-by-step explanation:

$Volume = Base \ Area\ * Height$

$Height = \frac{Volume}{Base \ Area}$

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

Putting in the formula

$Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}$

Doing long division, we get

$Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}$

$Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}$

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

Answer 2

Answer:

$x +1 - \frac{4}{x^3 + 3x^2 + 8}$

Step-by-step explanation:

$volume=base \: area \times height$

$height=\frac{volume}{base \: area}$

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

$h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}$

$h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}$

$h=x +1 - \frac{4}{x^3 + 3x^2 + 8}$