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Word Problems/Linear expressions


A rectangular prism has the volume, 18x^3-3x^2-6x. Write 3 possible linear expressions for the dimensions of the box.

Thank you in advance for your assistance, it is greatly appreciated.

Let x be 1, 2, and 3.  If x is any greater, the volume is almost a quarter million at x=4 and more than a million for x greater than 4.  The case where x = 1, 2, or 3 are, respectively,
9, 120, 3744.
For x=1, the 9 is gotten, and that could be 1x1x9.
For x=2, 120 is gotten, and that could be 2x2x30.
For x=3, 3744 is gotten, and that could be 12x12x26.

The prisms that I gave were square at one end, but they could just as easily be any numbers wanted as long as the products were 9, 120, and 3744.

For example, the one with volume 9 could be 1/3 x 9/4 x 12, for the volume is still 9.
As another exampe, the 3744 could be (only in theory), 10y x 10 x 3.744/y where y is any value.
The value of y could be 1, 3, 4.7, root(2), pi, 2.546346, etc. - most anything wanted.  

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Scott A Wilson


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