Answer:
The height of the prism is equal to [tex]h=(x^{3}-3x^{2}+5x-3)/(x^{2}-2)[/tex]
Step-by-step explanation:
we know that
The volume of a rectangular prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
In this problem we have
[tex]V=x^{3}-3x^{2}+5x-3[/tex]
[tex]B=x^{2}-2[/tex]
substitute in the formula and solve for h
[tex]x^{3}-3x^{2}+5x-3=(x^{2}-2)h[/tex]
[tex]h=(x^{3}-3x^{2}+5x-3)/(x^{2}-2)[/tex]
