Question

The volume of a rectangular prism is 2x3+9x2-8x-36 with height x + 2. Using synthetic division, what is the area of the base?

Answer 1

The answer is 2x2+5x-18. I know this is right because i passed my Algebra 2 class with a 98.

Answer 2

we know that

The volume of a rectangular prism as

`V=A*h`

where

V is volume

A is area

H is height

now, we are given

`V=2x^3+9x^2-8x-36`

`h=x+2`

now, we can find A

`V=A*h`

`A=(V)/(h)`

now, we can plug it

`A=(2x^3+9x^2-8x-36)/(x+2)`

now, we can synthetic division method

so, we can write it as

`A=(2x^3+9x^2-8x-36)/(x+2)=(2x^2+5x-18)`

so, the area of base is

`=(2x^2+5x-18)`.............Answer