4x^n+2-9x^n+6x^n-1-x^n-24x^(n+2)-9x^n+6x^(n-1)-x^(n-2),n是整数且大于2

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 22:53:38
4x^n+2-9x^n+6x^n-1-x^n-24x^(n+2)-9x^n+6x^(n-1)-x^(n-2),n是整数且大于24x^n+2-9x^n+6x^n-1-x^n-24x^(n+2)-9x^n

4x^n+2-9x^n+6x^n-1-x^n-24x^(n+2)-9x^n+6x^(n-1)-x^(n-2),n是整数且大于2
4x^n+2-9x^n+6x^n-1-x^n-2
4x^(n+2)-9x^n+6x^(n-1)-x^(n-2),n是整数且大于2

4x^n+2-9x^n+6x^n-1-x^n-24x^(n+2)-9x^n+6x^(n-1)-x^(n-2),n是整数且大于2
4x^(n+2)-9x^n+6x^(n-1)-x^(n-2)
=x^(n-2)*(4x^4-9x^2+6x-1)
=x^(n-2)*[(2x^2)^2-(3x-1)^2]
=x^(n-2)*(2x^2+3x-1)(2x^2-3x+1)
=x^(n-2)*(2x^2+3x-1)(x-1)(2x-1)

4x^n+2-9x^n+6x^n-1-x^n-2
=(4x^n+6x^n-9x^n-x^n)+(2-1-2)
=-1

4x^n+2-9x^n+6x^n-1-x^n-2
=x^n(4+6-9-1)+2-1-2
=-1