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

Answer:

x-1

Step-by-step 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