Answer
$(5q+2)(2q+1)$
Work Step by Step
Find factors of $ac$ that have a sum of $b$.
Since $ac=20$ and $b=9$,
find factors of $20 $ with a sum of $9$.
$\left[\begin{array}{lll}
\text{Factors of 20 } & \text{Sum of factors} & \\
1\text{ and }20 & 21 & \\
2\text{ and }10 & 12 & \\
4\text{ and }5 & 9 & \text{...what we needed}
\end{array}\right]$
$10q^{2}+9q+2$
...use the factors to rewrite $bx$.
$=10q^{2}+5q+4q+2$
...factor out the GCF out of each pair of terms.
$=5q(2q+1)+2(2q+1)$
...use the Distributive Property.
$=(5q+2)(2q+1)$
