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A rectangular prism has a volume of
4x(cubed) + 30 x(squared) +36x. What linear expressions can represent possible dimensions of the prism?

Please explain.

  • math -

    The volume factors into four linear factors:
    2x(x+6)(2x+3)
    Since we need three values for the dimensions of the prism, so there are
    C(4,2)=6 sets of dimensions, i.e. choose 2 factors out of 4 to reduce to one dimension. The two other dimensions will be used as is.
    Example dimensions are:
    2x (x+6) (2x+3)
    2 x(x+6) (2x+3)
    x 2(x+6) (2x+3)
    ...
    up to 6 sets.

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