A rectangular prism has a volume of 96 feet the area of the base is 24 feet what is the height of the prism

V=lhw

x (x+8) (x-2) = 96

x (x^2+6x-16) = 96

x^3+6x^2-16x-96=0 this is true when x=4 so (x-4) is a factor ...

(x^3+6x^2-16x-96) / (x-4)

x^2 rem 10x^2-16x-96

10x rem 24x-96

24 rem 0

(x-4) (x^2+10x+24) = 0

(x-4) (x^2+4x+6x+24) = 0

(x-4) (x (x+4) + 6 (x+4)) = 0

(x-4) (x+6) (x+4) = 0

x=-4,-6,4 since x>0 the only possible answer is

x=4

making the dimensions of the prism:

L=12ft, W=4ft, H=2ft

The height of the prism is 4 feet.