Ta có:
[tex]A=x^{2001}+x^{2000}+1=x^{2001}-x+x^{2000}-x^{2}+x^2+x+1\\ A=x(x^{2001}-1)+(x^{1998}-1)x^{2}+x^2+x+1[/tex]
[tex]x^{2001}-1=(x^3)667-1^{667}\vdots x^3-1\Rightarrow x^{2001}-1\vdots x^2+x+1\\ x^{1998}-1=(x^3)^{666}-1^{666}\vdots x^3-1\Rightarrow x^{1998}-1\vdots x^2+x+1\\ \Rightarrow A\vdots x^2+x+1[/tex]