First, , and if we multiply
by
we get
Subtracting this from the numerator gives a remainder of
Next, , and if we multiply
by
we have
and subtracting this from the previous remainder, we end up with a new remainder of
Next, , and if we multiply
by
we get
Subtracting from the previous remainder, we get a new remainder of
which contains no more factors of , so we're done.
So,