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.

Question

anonymous · Answer

Volume = length x width x height

If you have a known volume, length, and height; then you would solve for width.  So...

Width = V / (LH)

$$w=(x^3+9x^2+6x-16)/[(x+2)(x+8)]=(x^3+9x^2+6x-16)/(x^2+10x+6)$$

I use long division (I can't show that on here, so I'll leave that to you).  The width should be x - 1.  You can check by multiplying LWH to see if you get V.