把下列各式分解因式 x立方-3x+2 x⁴+4分之81 x⁴+x²y²+y⁴ x²y-7xy+6y

来源:学生作业学帮网 编辑:学帮网 时间:2024/07/02 03:02:47

把下列各式分解因式 x立方-3x+2 x⁴+4分之81 x⁴+x²y²+y⁴ x²y-7xy+6y

x^3-3x+2
=(x-1)(x^2+x-2)
=(x-1)(x+2)(x-1)
=(x+2)(x+1)^2
x^4+81/4
=(x^2+9/2)-(3x)^2
=(x^2+3x+9/2)(x^2-3x+9/2)
x^4+x^2y^2+y^4
=(x^2+y^2)-(xy)^2
=(x^2+xy+y^2)(x^2-xy+y^2)
x^2y-7xy+6y
=y(x^2-7x+6)
=y(x-6)(x-1)