GS. 2 Given that $x_{0}$ satisfies the equation $x^{2}+x+2=0$. If $b=x_{0}^{4}+2 x_{0}^{3}+3 x_{0}^{2}+2 x_{0}+1$, find the value of $b$.
By division,
$$
\begin{aligned}
b & =x_{0}^{4}+2 x_{0}^{3}+3 x_{0}^{2}+2 x_{0}+1 \\
& =\left(x_{0}^{2}+x_{0}+2\right)\left(x_{0}^{2}+x_{0}\right)+1=1
\end{aligned}
$$