The volume of a rectangular box can be represented buy the function V = 2x^3 - 11x^2 + 10x + 8

Question

The width is represented by the expression x-4. Determine the expressions for the height and length.

Answer 1

divide x-4 into the volume polynomial to get

2x^2-3x -2. Factor that into

(2x+1)(x-2)

the volume cubic factors into 3 factors

(x-4)(2x+1)(x-2)

those 3 factors are the sides of the rectangular box with

width = (x-4) and

height and length =

(2x+1) and (x-2)