\(x^4+2008x^2+2007x+2008=x^4+2008x^2+2008x+2008-x=\left(x^4-x\right)+2008\left(x^2+x+1\right)+x\left(x^3-1\right)=2008\left(x^2+x+1\right)+x\left(x+1\right)\left(x^2+x+1\right)=\left[\left(x+1\right)\left(x^2+x+2009\right)\right]\left(x^2+x+1\right)\)