Dear students,

as Tyler Bosmeny pointed out, it is not defined in Problem 3 of the problem set what is the degree of the zero polynomial.

There is not a universally accepted way to assign a degree to the zero polynomial. For this exercise you can consider the polynomial zero to have
all degrees (i.e. the identity deg0=n holds for every integer n).

Other possible choices are:
deg0=0
deg0=-1
deg0= minus infinity
(In fact, for all the above choices you will end up to the same answers to the questions in problem 3)

Sincerely,

Alberto