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