\(x^4+2007x^2+2006x+2007\)
\(=x^4+2007x^2+2007x-x+2007\)
\(=\left(x^4-x\right)+\left(2007x^2+2007x+2007\right)\)
\(=x\left(x^3-1\right)+2007\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2007\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2007\right)\)