So the remainder must be -2.
Hello, this is a problem from Israel Gelfand's Algebra book about polynomials.
Problem 152. The polynomial gives a remainder of when divided by . Find the remainder when is divided by .
My try: We know that where Q is the quotient, this is the same as , I see that all I have to do is to rewrite this equation to something like this , I tried dividing both sides by but I can't get the form of .
Thanks in advance.
Remember that remainder is always less than the divisor, this is a little difficult to formalize in case of polynomials rather than in case of numbers. I think, a remainder when divided with a linear polynomial would be a constant, the acceptable remainder when you divide using a quadratic (like x^2 - 1) would be a linear polynomial (5x - 7) or a constant. Keep this in mind, and you will be able to factorize out correctly.