Question

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.

Answer 1

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