\(x^4+2010x^2+2009x+2010\\ =\left(x^4-x\right)+\left(2010x^2+2010x+2010\right)\\ =x\left(x^3-1\right)+2010\left(x^2+x+1\right)\\ =x\left(x-1\right)\left(x^2+x+1\right)+2010\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^2-x+2010\right)\)
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x4+2010x2+2009x+2010
=x4+2010x2+2010x-x+2010
=(x4-x)+(2010x2+2010x+2010)
=x(x3-1)+2010(x2+x+1)
=x(x-1)(x2+x+1)+2010(x2+x+1)
=(x2+x+1)[x(x2-1)+2010]
=(x2+x+1)(x2-x+2010)
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