Answer
$3,4,6,8,12,24$
Work Step by Step
We are given:
$x$
$x-1$
$x-2$
and $V=24$
The volume of the prism is given by:
$V=x(x-1)(x-2)$
then
$x(x^2-2x-x+2)=24$
$x^3-3x^2+2x-24=0$
Possible rational zeros: $\pm 1,\pm 2, \pm 3, \pm4, \pm 6, \pm 8, \pm 12, \pm 24$
Since x represents a dimension, it must be positive. Otherwise, it can not be $1,2$. So the possible rational solutions of the equation are $3,4,6,8,12,24$
