\(x\left(x+1\right)\left(x^2+x+1\right)-42\)
\(=\left(x^2+x\right)\left(x^2+x+1\right)-42\)
Đặt \(x^2+x=t\)
\(=t\left(t+1\right)-42\)
\(=t^2+t-42\)
\(=t^2-6t+7t-42\)
\(=t\left(t-6\right)+7\left(t-6\right)\)
\(=\left(t-6\right)\left(t+7\right)\)
\(=\left(x^2+x-6\right)\left(x^2+x+7\right)\)
\(=\left(x-2\right)\left(x+3\right)\left(x^2+x+7\right)\)