Answer:
[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]
Step-by-step explanation:
Let
h------> the height of the prism
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
In this problem we have
[tex]V=x^{4}+4x^{3}+8x+4[/tex]
[tex]B=x^{3}+3x^{2}+8[/tex]
substitute and solve for h
[tex]x^{4}+4x^{3}+8x+4=(x^{3}+3x^{2}+8)h[/tex]
[tex]h=(x^{4}+4x^{3}+8x+4)/(x^{3}+3x^{2}+8)[/tex]
