we know that
The volume of a rectangular prism as
[tex]V=A*h[/tex]
where
V is volume
A is area
H is height
now, we are given
[tex]V=2x^3+9x^2-8x-36[/tex]
[tex]h=x+2[/tex]
now, we can find A
[tex]V=A*h[/tex]
[tex]A=\frac{V}{h}[/tex]
now, we can plug it
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}[/tex]
now, we can synthetic division method
so, we can write it as
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}=(2x^2+5x-18)[/tex]
so, the area of base is
[tex]=(2x^2+5x-18)[/tex].............Answer
