Hint for exercise 9 of Sec 2.3

 

Some sort of lexicographic order will do the job, but the "usual" ordering of the variables, i.e.,  x > y > z,   will not work.
So, we have to permute the ordering of the variables somehow.
 
Given that we want the remainder to be a polynomial in  x  alone, which variable has to be last in our revised ordering??
 


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