Question

因式分解x四次方+1991x平方+1990x+1991

Answer 1

式中数字较大且相近,不妨从一般式考虑

设1990=n

原式

=x^4+(n+1)x²+nx+n+1

=x^4+nx²+x²+nx+n+1

=(x^4+x²+1)+(nx²+nx+n)

=[(x^4+2x²+1)-x²]+n(x²+x+1)

=[(x²+1)²-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+1991)