Question

x^4+2008x^2+2007x+2008

 

Answer 1

x^4+2008x^2+2007x+2008

=x^4+2008x^2+2008x+2008-x

=x(x^3-1)+2008(x^2+x+1)

=x(x-1)(x^2+x+1)+2008(x^2+x+1)

=(x^2+x+1)(x^2-x+2008)

Answer 2

x⁴+2008x²+2007x+2008

=(x⁴+x²+1)+(2007x²+2007x+2007)

=(x⁴+2x²+1-x²)+2007(x²+x+1)

=(x²+1)²-x²+2007(x²+x+1)

=(x²+1-x)(x²+1+x)+2007(x²+x+1)

=(x²+x+1)(x²+1-x+2007)=(x²+x+1)(x²-x+2008)