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

1. ## 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 $x$, the width is $x-4$, and the height is $x-1$.

The wedge's length is $x-5$, width is $2$, and the height is $2$.

volume=lengthxwidthxheight

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

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

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

Is this right?

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