分解因式(1)m^2(m-n)-4(n-m)^2(2)2a(x-y)^3+2a^3(y-x)(3)-2x^3+3x^2-x(4)-x^n+4+x^n+12.如果3x^2-4x+2m在实数范围内可分解因式,求m的取值范围?

Question

分解因式
(1)m^2(m-n)-4(n-m)^2
(2)2a(x-y)^3+2a^3(y-x)
(3)-2x^3+3x^2-x
(4)-x^n+4+x^n+1
2.如果3x^2-4x+2m在实数范围内可分解因式,求m的取值范围?

Answer 1

(1)m^2(m-n)-4(n-m)^2=-m^2(n-m)-4(n-m)^2=(n-m)(-m^2-4(n-m))
(2)2a(x-y)^3+2a^3(y-x)=2a(x-y)^3-2a^3(x-y)=(x-y)(2a(x-y)^2-2a^3)
(3)-2x^3+3x^2-x=-x(2x^2-3x+1)=-x(2x-1)(x-1)
(4)-x^(n+4)+x^(n+1)=x^(n+1)(1-x^3)