Question

23. Using factor theorem, show that (x - y)is a factor of x(y2 - z2) + y(z2 – x2) + z(x2 - y2).
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Answer 1

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