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Thread: Write a Polynomial V(x) for the Remaining Part of the Solid

  1. #1
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    Write a Polynomial V(x) for the Remaining Part of the Solid

    All distances in the figure are in feet.
    A wedge is cut from a rectangular solid.
    The rectangular solid's length is [tex]x[/tex], the width is [tex]x-4[/tex], and the height is [tex]x-1[/tex].

    The wedge's length is [tex]x-5[/tex], width is [tex]2[/tex], and the height is [tex]2[/tex].

    volume=lengthxwidthxheight

    So what I did was get the volume of the wedge first:
    V=[tex](x-5)(2)(2)[/tex]
    V=[tex](4)(x-5)[/tex]
    V=[tex]4x-20[/tex]

    Then I did the whole solid:
    V=[tex](x)(x-4)(x-1)[/tex]
    V=[tex](x^2-4x)(x-1)[/tex]
    V=[tex]x^3-1x^2-4x^2+4x[/tex]
    V=[tex]x^3-5x^2+4x[/tex]

    Then I subtracted the volume of the wedge from the volume of the whole solid:
    V=[tex]x^3-5x^2+4x-4x-20[/tex]
    V=[tex]x^3-5x^2-20[/tex]

    Is this right?

  2. #2
    You have not supplied a figure. Is the wedge a horizontal prism?

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