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.

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