$A=x^{100}-2021x^{99}+2021x^{98}+...+2021x^2-2021x+2021$
$=x^{100}-2020x^{99}-x^{99}+2020x^{98}+...+x^2-2020x-x+2021$
$=x^{99}(x-2020)-x^{98}(x-2020)+...+x(x-2020)-x+2021$
Thay $x=2020$ vào $A$, ta có:
$A=2020^{99}.0-2020^{98}.0+...+2020.0-2020+2021$
$\to A=1$