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

The possible dimensions of the rectangle are $2x+3$ and $4x+5$.
Find factors of $ac$ that have a sum of $b$. Since $ac=120$ and $b=22$, find positive factors of $120$ with a sum of $22$. $\left[\begin{array}{lll} \text{Factors of 120 } & \text{Sum of factors} & \\ 1\text{ and }120 & 121 & \\ 2\text{ and }60 & 62 & \\ 3\text{ and }40 & 43 & \\ 4\text{ and }30 & 34 & \\ 5\text{ and }24 & 29 & \\ 6\text{ and }20 & 26 & \\ 8\text{ and }15 & 23 & \\ 10\text{ and }12 & 22 & \text{is what we need} \end{array}\right]$ $8x^{2}+22x+15$ ...use the factors to rewrite $bx$. $=8x^{2}+10x+12x+15$ ...factor out the GCF out of each pair of terms. $=2x(4x+5)+3(4x+5)$ ...use the Distributive Property. $=(2x+3)(4x+5)$