\(x=2009\)
\(\Rightarrow x-1=2008\left(1\right)\)
Thay (1) vào A ta được:
\(A=x^{2009}-2008x^{2008}-2008x^{2007}-...-2008x+1\)
\(A=x^{2009}-\left(x-1\right)x^{2008}-...-\left(x-1\right)x+1\)
\(A=x^{2009}-x^{2009}+x^{2008}-...-x^2-x+1\)
\(A=-x+1\)
\(A=-2009+1\)
\(A=-2008\)