已知多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z各项的公因式是2x^3y^4z,求m,n

已知多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z各项的公因式是2x^3y^4z,求m,n
已知多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z各项的公因式是2x^3y^4z,求m,n

已知多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z各项的公因式是2x^3y^4z,求m,n
多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z各项的公因式是2x^3y^4z,
m=4
n-2=3
m=4,n=5

多项式4x^n y^m z+2x^n-1 y^m+2 z^2+6x^n-2 y^m+1 z
=2x^-2 y^m z
即：2x^n-2 y^m z=2x^3 y^4 z
∴n=5 m=4