数学题目:2004X^3 + 2005X^2 - 2006X +2007 谁会做?

问题描述:

数学题目:2004X^3 + 2005X^2 - 2006X +2007 谁会做?
2004X^3 + 2005X^2 - 2006X +2007
化解!

原式=2004x^3+2005x^2-2004x-2x+2005+2
=2004x^3-2004x+2005x^2+2005-2x+2
=2004x(x^2-1)+2005(x^2-1)-2(x-1)
=2004x(x+1)(x-1)+2005(x+1)(x-1)-2(x-1)
=(2004x^2+2004x+2005-2)(x-1)
=2004(x^2+x-2)(x-1)
=2004(x+2)(x-1)(x-1)