# How do you factor 3x^2+5x+2?

The only (positive) factors of $3$ are $\textcolor{b l u e}{3 \times 1}$
The only (positive) factors of $2$ are $\textcolor{red}{2 \times 1}$
The coefficient of the middle term, $5$ can be written as $\textcolor{b l u e}{3} \times \textcolor{red}{1} + \textcolor{red}{2} \times \textcolor{b l u e}{1}$
$3 {x}^{2} + 5 x + 2 = \left(\textcolor{red}{3 x} + \textcolor{red}{2}\right) \left(\textcolor{b l u e}{1 x} + \textcolor{b l u e}{1}\right)$