Question

The volume of a rectangular prism is 2x^3+9x^2-8x-36 with height x + 2. Using synthetic division, what is the area of the base?

Answer 1

Answer:

Area of the base = $2x^2+5x-18$

Step-by-step explanation:

We know that volume of rectangular prism = (Area of base) x (Height)

or [Area of base] = [Volume]/[Height]

So basically we need to divide given area by given height to find the answer.

given height is (x+2) that means (x+2) must be factor of volume equation

or x=-2 must be root of volume equation so write down coefficients of volume equation then we divide by -2 as shown in attached picture.

Last digit on the right is always remainder.

Remaining coefficients {2, 5, -18} will give the area equation: $2x^2+5x-18$

Hence final answer is:

Area of the base = $2x^2+5x-18$