Posted by **Shadow** on Tuesday, February 7, 2012 at 9:05pm.

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

- Algebra -
**Reiny**, Tuesday, February 7, 2012 at 11:02pm
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

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