\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+\left(x+6\right)\left(x-1\right)\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+x^2+5x-6\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24+x^2+5x-6\)
\(=\left(x^2+5x\right)^2+11\left(x^2+5x\right)+18\)
\(=\left(x^2+5x+9\right)\left(x^2+5x+2\right)\)