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

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

Performing polynomial division:
(x^4 + 4x^3 + 3x^2 + 8x + 4) ÷ (x^3 + 3x^2 + 8) = x + 1 - 4/(x^3 + 3x^2 + 8).

So the height is x + 1 - 4/(x^3 + 3x^2 + 8).