Hello,

The remainder has to be a polynomial ofat mostdegree 1.

This means that it is in the form R(x)=ax+b, where a and b can be equal to 0.

Let's denote and note that

What we'll do is studying the zeroes of the polynomials...

We have

where Q is the quotient.

If we let x=1, we have

Thus

If we differentiate, we have

But and

Again, if we let x=1, the red part will be equal to 0.

Which gives

Thus b=... and the remainder R is...