Question

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.

Answer 1

x^2-2x-9

Explanation:

Answer 2

The volume of a rectangular prism is this
Volume = Area x Height
Substituting the given expressions
x3 + 2x2 - 17x - 36 = Area x (x + 4)
Area = (x3 + 2x2 - 17x - 36) / (x + 4)
Now, let's use synthetic division
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0

The expression for the area is
Area = x2 - 2x - 9