Example. Factorization: $x^{7}+2 x^{5}+x+2$.
$$
\begin{array}{l}
x^{7}+2 x^{5}+x+2=\left(x^{7}+x^{5}+1\right) \\
+\left(x^{5}+x+1\right)=\left(x^{2}+x+1\right) \\
\left(x^{5}-x^{4}+2 x^{3}-x^{2}-x+2\right)
\end{array}
$$
(Author's affiliation: Dao County No.1 High School, Hunan)
