\(=\left(x^4-x^3+2011x^2\right)+\left(x^3-x^2+2011x\right)+\left(x^2-x+2011\right)=x^2\left(x^2-x+2011\right)+x\left(x^2-x+2011\right)+\left(x^2-x+2011\right)=\left(x^2+x+1\right)\left(x^2-x+2011\right)\)
\(=\left(x^4-x\right)+\left(2011x^2+2011x+2011\right)\\ =x\left(x^3-1\right)+2011\left(x^2+x+1\right)\\ =x\left(x-1\right)\left(x^2+x+1\right)+2011\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^2-x+2011\right)\)
Lời giải:
$x^4+2011x^2+2010x+2011$
$=(x^4-x)+(2011x^2+2011x+2011)$
$=x(x^3-1)+2011(x^2+x+1)$
$=x(x-1)(x^2+x+1)+2011(x^2+x+1)$
$=(x^2+x+1)(x^2-x+2011)$
