答案:(x^2+x+1)(x^2-x+1997)
x^4+1997x^2+1996x+1997
=x^4+1997x^2+1997x-x+1997
=(x^4-x)+(1997x^2+1997x+1997)
=x(x^3-1)+1997(x^2+x+1)
=x(x-1)(x^2+x+1)+1997(x^2+x+1)
=(x^2+x+1)(x^2-x+1997)