## Algebra 1: Common Core (15th Edition)

The possible dimensions of the prism are $4c,\ c+8$ and $c+5$.
$4c^{3}+52c^{2}+160c$ ...factor out the GCF. $=4c(c^{2}+13c+40)$ ...find factors of $ac$ that have a sum of $b$. ($ac=40,\ b=13$) $\left[\begin{array}{lll} \text{Factors of 40 } & \text{Sum of factors} & \\ 1\text{ and }40 & 41 & \\ 2\text{ and }20 & 22 & \\ 4\text{ and }10 & 14 & \\ 5\text{ and }8 & 13 & \text{ is what we need } \end{array}\right]$ ...use the factors you found to rewrite $bc$. $=4c(c^{2}+5c+8c+40)$ ...factor by grouping. $=4c[c(c+5)+8(c+5)]$ ...use the Distributive Property. $=4c(c+8)(c+5)$ The possible dimensions of the prism are $4c,\ c+8$ and $c+5$.