\(\times^2+7\times+12\)
\(=(\times^2+4\times)+\left(3\times+12\right)\)
\(=\times\left(\times+4\right)+3\left(\times+4\right)\)
\(=\left(\times+4\right)\left(\times+3\right)\)
\(x^2+7x+12=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)