x^4+1998x^2+1997x+1998用换元法因式分解用换元法解,知道的回答下谢谢!

Question

x^4+1998x^2+1997x+1998用换元法因式分解
用换元法解,知道的回答下谢谢!

Answer 1

不知道对不对,
设1997=n
原式
=x^4+(n+1)x²+nx+(n+1)
=(x^4+x²+1)+(nx²+nx+n)
=[(x^4+2x²+1)-x²]+n(x²+x+1)
=[(x²+1)-x²]+n(x²+x+1)
=(x²+x+1)(x²-x+1)+n(x²+x+1)
=(x²+x+1)(x²-x+n+1)
=(x²+x+1)(x²-x+1988)