[tex]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}[/tex]
Answer:
Height = [tex]\frac{(x+3)(x^{3}+x^{2}+8)}{(x^{3}+3x^{2}+8)}[/tex]
Step-by-step explanation:
The volume of a rectangular prism = [tex](x^{4}+4x^{3}+3x^{2}+8x+4)[/tex]
and the area of the base = ([tex](x^{3}+3x^{2}+8)[/tex]
We know the formula,
Volume of the rectangular prism = Area of the base × Height
Height = [tex]\frac{\text{Volume of the prism}}{\text{Area of the base}}[/tex]
Now plug in the value of volume and area in the formula
Height = [tex]\frac{x^{4}+4x^{3}+3x^{2}+8x+24}{x^{3}+3x^{2}+8}[/tex]
Further solving the fraction
Height = [tex]\frac{(x+3)(x^{3}+x^{2}+8)}{(x^{3}+3x^{2}+8)}[/tex]
