Example 1. Factorize: $2 x^{3}-x^{2}-x-3$.


Solve $\begin{aligned} & 2 x^{3}-x^{2}-x-3 \\ = & 2 x^{3}+2 x^{2}+2 x-3 x^{2} \cdots 3 x-3 \\ = & \left.2 x i x^{2}+x+1\right)-3\left(x^{2}+x+1\right) \\ = & (2 x-3)\left(x^{2}+x+1\right)\end{aligned}$