When the coefficient of $x^2$ is 1, you can often factorise by inspection. When it is not 1, as in $2x^2+7x+3$, splitting the middle term is the reliable method.

For an expression of the form $a{x}^2+bx+c$, first check for a common factor. If there is none, multiply $a$ and $c$, then find two numbers that multiply to $ac$ and add to $b$.