volume of rectangular prism

Question

If the volume of a rectangular prism is 2x³ - 2x² - 40x, and if its width is 3x, and its height is x + 4, what is its length?

Answer 1

Volume = V = 2x^3 -2x^2 -40x = 2x(x^2 -x -20) = 2x(x-5)(x+4)

V= hLW

L = V/hW = (2x)(x-5)(x+4))/3x(x+4)

L = (2/3)(x-5)/(x+4) = Length of the rectangular prism

that's probably the answer you want.

or

you could make the division by long hand or synthetic division and get

L = (3/2)(1 - 9/(x+4))

or

L = 3/2 - 27/2(x+4)

or

L = 1.5 - 13.5/(x+4)

or 1.5 - 27/(2x+8)

they're all equivalent

Answer 2

(2x³ - 2x² - 40x) / (3x)(x + 4) = L