\(=x\left(x+2\right)\left(x+1\right)\left(x+3\right)-24\)
\(=x\left(x+3\right)\left(x+1\right)\left(x+2\right)-24\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-24\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)-24\)
\(=\left(x^2+3x\right)^2-4\left(x^2+3x\right)+6\left(x^2+3x\right)-24\)
\(=\left(x^2+3x\right)\left(x^2+3x-4\right)+6\left(x^2+3x-4\right)\)
\(=\left(x^2+3x-4\right)\left(x^2+3x+6\right)\)
\(=\left(x-1\right)\left(x+4\right)\left(x^2+3x+6\right)\)