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

Dividing the volume by the base area, you find the height to be ...
$\frac{x^{4}+4x^{3}+3x^{2}+8x+4}{x^{3}+3x^{2}+8}=x+1-\frac{4}{x^{3}+3x^{2}+8}$

The height of the prism is $x+1-\frac{4}{x^{3}+3x^{2}+8}$

Answer 2

Solution:

Volume of Rectangular Prism = $x^4 + 4 x^3 + 3 x^2 + 8 x + 4$

Area of Base of Prism = $x^3 + 3 x^2 + 8$

As Given:

→→Volume of Rectangular Prism = Base Area ×  Height

→Height of Prism = $\frac{\text{Volume of Rectangular Prism}}{Base Area}$

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

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