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

$\left(2 x + 3\right) \left(x + 1\right)$
There are $2$ numbers that can multiply together and add to $5$.
If you use $2 \times 1$ and $3 \times 1$ you can add those numbers together and add to $5$.
$\left(2 x + 3\right)$
$\left(x + 1\right)$