The volume in cubic feet of a box can be expressed as (x) = x^3-6x^2+8x, or as the product of three linear factors with integer coefficients. The width of the box is x-2. Factor the polynomial to find linear expressions for the height and the length. Show your work.

Volume of the vox: V (x) = x^3-6x^2+8x

V (x) = W (x) H (x) L (x)

Width: W (x) = x-2

Height: H (x) = ?

Length: L (x) = ?

Factoring the equation of Volume:

V (x) = x^3-6x^2+8x

Common factor x:

V (x) = x (x^3/x-6x^2/x+8x/x)

V (x) = x[x^ (3-1) - 6x^ (2-1) + 8]

V (x) = x (x^2-6x+8)

V (x) = x (x-2) (x-4)

V (x) = W (x) H (x) L (x)

We know that W (x) = x-2

Then we have two options for H (x) and L (x):

1) First option: L (x) = x and H (x) = x-4

or

2) Second option: L (x) = x-4 and H (x) = x