Question

The volume of a rectangular prism is (x4 + 4x^3 + 3x^2 + 8x + 4), and the area of its base is (x3 + 3x^2 + 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

$V=x^4+4x^3+3x^2+8x+4\\\\B=x^3+3x^2+8\\\\V=BH\to H=\dfrac{V}{B}\\\\\text{Substitute:}\\\\H=\dfrac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}$

Answer 2

Answer:

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

Step-by-step explanation:

The volume of a rectangular prism = $(x^{4}+4x^{3}+3x^{2}+8x+4)$

and the area of the base = ($(x^{3}+3x^{2}+8)$

We know the formula,

Volume of the rectangular prism = Area of the base × Height

Height = $\frac{\text{Volume of the prism}}{\text{Area of the base}}$

Now plug in the value of volume and area in the formula

Height = $\frac{x^{4}+4x^{3}+3x^{2}+8x+24}{x^{3}+3x^{2}+8}$

Further solving the fraction

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