\(\Rightarrow\left\{{}\begin{matrix}x+1=21\\x+2=22\end{matrix}\right.\)
\(\Rightarrow P=x^{2021}-\left(x+1\right)x^{2020}+\left(x+1\right)x^{2019}-\left(x+1\right)x^{2018}+...+\left(x+1\right)x-\left(x+2\right)\)
\(=x^{2021}-x^{2021}-x^{2020}+x^{2020}+x^{2019}-x^{2019}-x^{2018}+...+x^2+x-x-2\)
\(=-2\)