Answer to Question #10922 in Algebra for nistala ks prasad

Question

using factor theorem show that x-y, y-z, z-x are the factors of x(y^2-z^2) + y(z^2-x^2) + z(x^2-y^2)

Answer 1

to show that x-y is the factor we must substitute x=y
y*(y^2-z^2) +
y(z^2-y^2) + z(y^2-y^2)=0 so x-y is the factor of polynom

to check y-z
and z-x we must substitute y=z and z=x correspondently and we get also 0 so
there are the factors