Question

Using factor theorem, show that (x - y)is a factor of x(y^2 - z^2) + y(z^2 – x^2) + z(x^2 - y^2).​

Answer 1

Step-by-step explanation:

x(y2−z2)+y(z2−x2)+z(x2−y2)=xy2−xz2+yz2−yx2+zx2−zy2

Arrange the terms in descending order of power of x.

=−x2y+zx2+xy2−xz2−yz+yz2

=−x2(y−z)+x(y2−z2)−yz(y