Question

The volume in cubic feet of a Cd holder can be expressed as V(x)=-x^3-x^2+6x, the depth is 2-x , factor the polynomial to find linear expression for the height and the width. - Do I just factor the -x^3-x^2+6x? It because I know the volume is LWH, so don't I have to subtract the depth from the volume? Thanks

Answer 1

volume = length x width x height
so
-x^3 - x^2 + 6x = (length x width) x (2-x)
multiply each side by -1

x^3 + x^2 - 6x = (length x width) x (x-2)
do either a long divsion or use synthetic division to get

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

so the height is (2-x) , that was given
the length is x+3
the width is x

check:
multiply x(2-x)(x+3) to get -x^3 - x^2 + 6x