SOLUTION: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor. PLEASE HELP ME!!!!!!

We use the fact that if a number is substituted for x 
in a polynomial, the result is the same as the remainder 
left when that polynomial is divided by x minus that number.

So we substitute  in the polynomial to see if the
remainder is 0, and if it is then we'll know that if we 
had divided the polynomial by , the reaminder
would be 0, making  a factor:

So we substitute  into the polynomial:






and everything cancels out and we have

0

so 0 would be the remainder if 



were divided by , so 

 is a factor of  .

And of course  is linear because the highest power
of x is 1.

Edwin