The volume of a rectangular prism is (x^4+4x^3+3x^2+8x+4), and the area of its base is (x^3+ 3x^2+8). 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 = area * height => height = volume / area

2)

                  x^4 + 4x^3 + 3x^2 + 8x + 4
height =   
                           x^3 + 3x^2 + 8

That division is not exact

The result of this division is x + 1 plus a residue of - 8x^2 + 8x - 4.

It was expected an exact division, so likely some of the terms is not properly written. Now you know the procedure and can perform it with the right terms.