SOLUTION: When a polynomial P(x) is divided by D(x), its quotient is Q(x) and remainder is R(x). Is it true that when P(x) is divided by Q(x), its remainder is also R(x)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: When a polynomial P(x) is divided by D(x), its quotient is Q(x) and remainder is R(x). Is it true that when P(x) is divided by Q(x), its remainder is also R(x)?      Log On


   

Question 200667: When a polynomial P(x) is divided by D(x), its quotient is Q(x) and remainder is R(x). Is it true that when P(x) is divided by Q(x),
its remainder is also R(x)?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Nope.
Make it easy on yourself, forget the polynomials and try the problem using integers. Take an instance and see if it works, If it won;t work for numbers, it wont work for polynomials
So, let's take 20/6
result 3 1/3
Now take 20/3
result 6 2/3
1/3 <> 2/3 so you can see they are not equal. If there is a speficic case where the proposal fails to hold, then it cannot hold in general
So in one easy step you found a case where the proposed answer fails. All it takes is one !