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Question
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
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Solution
If x - y is assumed to be fsctor, then x = y. Substituting this in problerr polynomial, we get :
f(x = y) = yz (y2 - z2) + zy(z2 - y2) + yy (y2 - y2)
= yz (y2-z2) + zy(-(y2 - z2)) + 0
= yz (y2 - z2) - yz (y2 - z2) = 0
Hence , (x - y) is a factor.
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