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Algebra

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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 -

    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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