Geometry question. Rectangular prism

A rectangular prism has a volume of 3x²+18x+24. Its base has a length of x+2 and a width of 3. What is the height of the prism?

We have V = 3x^2 + 18x + 24, b = x + 2, and w = 3. Clearly, V = bwh, so
bwh = 3x^2 + 18x + 24
If we sub b = x+2, and w = 3 into the above eqn:
3(x+2)h = 3x^2 + 18x + 24
Now solve for h:
(x+2)h = (3x^2 + 18x + 24) / 3 = x^2 + 6x + 8
h = (x^2 + 6x + 8) / (x + 2)
h = x + 4

V=length.width.height
height=V/(length.width)
height=(3x^2+18x+24)/(3*(x+2))=x+4