\(x^4+2010x^2+2009x+2010\)
\(=x^4-x+\left(2010x^2+2010x+2010\right)\)
\(=x\left(x^3-1\right)+2010\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2010\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+2010\right]=\left(x^2+x+1\right)\left(x^2-x+2010\right)\)