###### Example7.4.4

Factor $$10x^2+23x+6\text{.}$$

1. $$10\cdot6=60$$

2. Use a list of factor pairs for $$60$$ to find that $$3$$ and $$20$$ are a pair that sums to $$23\text{.}$$

3. Intentionally break up the $$23$$ as $$3+20\text{:}$$

\begin{align*} \amp10x^2\overbrace{{}+23x}+6\\ \amp=10x^2\overbrace{{}+3x+20x}+6\\ \amp=\left(10x^2+3x\right)+(20x+6)\\ \amp=x\highlight{(10x+3)}+2\highlight{(10x+3)}\\ \amp=\highlight{(10x+3)}(x+2) \end{align*}
in-context