Answer
The possible dimensions of the rectangle are
$2x+3$ and $4x+5$.
Work Step by Step
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.
$=(2x+3)(4x+5)$
