Finding the Remainder in Division of Polynomials | Step-by-Step Solution

[Ahmed Abdullah]

What is the remainder??

Homework Statement

What is the remainder when (a+b+c)^333-a^333-b^333-c^333 is divided by (a+b+c)^3-a^3-b^3-c^3?

Homework Equations

None

The Attempt at a Solution

I tried this
(a+b+c)^333-a^333-b^333-c^333 = Q{(a+b+c)^3-a^3-b^3-c^3}+h

where h is the remainder
I proceeded further but only managed to work out that Q>(a+b+c)^330.
I don't know how to attack this types of problem.
Please help!

 

[StatusX]

Are these polynomials in the variables a,b,c? If so, I don't think there's a natural way to talk about remainders. You first have to define a norm on the set of polynomials. For example, you could take it to be the largest power of a (or b, or c, which is what I mean by when I say there's no natural way).

 

[Gib Z]

Why Don't you just do it by hand? :p