The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). if the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

1) Volume = x^3 - 3x^2 + 5x - 3

2) Area of the base = x - 2

3) Volume = base area * height =>

4) height = volume / base area = (x^3 - 3x^2 + 5x - 3) / (x - 2)

So, you have to divide the polynomial x^3 - 3x^2 + 5x - 3 by the polynomial x - 2 to find the height.

5) I will use short division:

    |1    - 3    +  5    - 3
    |
 2 |      + 2    -  2    +6

     1    - 1     + 3      +3

That division left remainder + 3.

The quotient is x^2 - 3x + 3.

The reaminder (3) indicates that the polynomilar x^3 - 3x^2 + 5x - 3 is not divisible by x - 2, and that means that you cannot find the exact height.

I suggest that you check the numbers of the statement because most likely there is an error. Nevertheless, this explanation of the detailed procedure to determine the height fo the prism by dividing the volumen by the base area is complete and detailed enough to calculate the answer.

The third and fourth box.