Answer
The possible dimensions of the prism are $2x,\ 5x+2$ and $6x+1$.
Work Step by Step
$60x^{3}+34x^{2}+4x=$
...factor out the GCF.
$=2x(30x^{2}+17x+2)$
...find factors of $ac$ that have a sum of $b$.
($ac=60,\ b=17$)
$\left[\begin{array}{lll}
\text{Factors of 60 } & \text{Sum of factors} & \\
1\text{ and }61 & 62 & \\
2\text{ and }30 & 32 & \\
3\text{ and }20 & 23 & \\
4\text{ and }15 & 19 & \\
5\text{ and }12 & 17 & \text{ is what we need}
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=2x(30x^{2}+5x+12x+2)$
...factor by grouping.
$=2x[5x(6x+1)+2(6x+1)]$
...use the Distributive Property.
$=2x(5x+2)(6x+1)$
The possible dimensions of the prism are $2x,\ 5x+2$ and $6x+1$.
