Using factor theorem, show that x-y, y-z, z-x are the factors of x2(y-z)+y2(z-x)+z2(x-y)

Answer :

We know Factor theorem " ​When x-c is a factor of the polynomial then f(c)=0 . "
So 
We have polynomial  = x2) + y2(zx ) + z2x)
So according to factor theorem if ( x ) is factor of our polonomial so it gives it value zero at xy 
We substitute xy  , And get
y2yz ) + y2(zy) + z2yy )
y3y2zy2zy3 + 0
= 0
So ( x) is a factor of our polynomial.

Now check for ( y) is a factor of our polynomial or not
So we substitute z , And get
x2 - ) + z2(z - x ) + z2x - )​

= 0 + z3 - z2x + z2x - z3
= 0
So ( y - ) is a factor of our polynomial.

Now check for ( z - ) is a factor of our polynomial or not
So we substitute  z  = x , And get​

x2 - ) + y2(x - x ) + x2x - )​
x2yx3 + 0 + x3x2y 

= 0

So ( z - ) is a factor of our polynomial.

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