Question

using factor theorem show that (x-y) is a factor of x(y² -z² ) +y(z²-x² )+ z(x²-y²) 

Answer 1

Let x-y is a factor
Then x = y

> x(y² -z² ) +y(z²-x² )+ z(x²-y²)
= x(x²-z²) + x(z²-x²) + z(x²-x²)
= x³ - xz² + xz² - x³ + z(0)
= 0 + 0
= 0

The remainder is zero.
So, x-y is a factor of x(y² -z² ) +y(z²-x²) + z(x²-y²)

Hence proved

Answer 2

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