初二 数学 因式分解 请详细解答,谢谢! (17 11:17:0)

x4+2001x2+2000x+2001
= x4+2001x2+2001x-x+2001
=(x4-x)+2001x2+2001x+2001
=x(x^3-1)+2001(x2+X+1)
=x(x-1)(x^2+x+1)+2001(x2+x+1)
=(x^2-x+2001)(x^2+x+1)
^2是平方，这里用到立方差公式a^3-b^3=(a-b)(a^2+ab+b^2)

原式＝x^4-x^3+x^3+2001x^2-x^2+x^2+2001x-x+2001
=(x^4-x^3+2001x^2)+(x^3-x^2+2001x)+(x^2-x+2001)
=x^2(x^2-x+2001)+x(x^2-x+2001)+(x^2-x+2001)
=(x^2+x+1)(x^2-x+2001)

(2001 - x + x^2) (1 + x + x^2)

(2001 - x + x^2) (1 + x + x^2)