Question

The volume of a rectangular prism is represented by the function x3 + 9x2 + 6x – 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box.

Answer 1

x-1

Explanation:

x^3 + 9x^2 + 6x - 16 = (x + 2)

(x + 8) = (x^2 + 10x + 16)

-2 1 9 6 -16

-2 -14 16

-8 1 7 -8 0

-8 8

1 -1 0

x^3 + 9x^2 + 6x - 16 = (x + 2)(x + 8)(x - 1)

Answer 2

The volume of the box is length * width * height
x^3 + 9x^2 + 6x - 16 = (x + 2) * width * (x + 8) = (x^2 + 10x + 16) * width
using synthetic division
-2 1 9 6 -16
-2 -14 16

-8 1 7 -8 0
-8 8

1 -1 0

Therefore, x^3 + 9x^2 + 6x - 16 = (x + 2)(x + 8)(x - 1)
Therefore, the width of the prism is x - 1