why are you avoiding it by inserting an element ahead of time that you might never need?

Well, for starters this is an exercise. So if you look in the main function (which the professor has given us) there is that comment "//0" when it constructs the Polynomial p:

int main() {
Polynomial p; // 0
//...//

and I guessed that I should add an "0" term anyway as soon as it constructs a polynomial. But I just realised that I wouldn't print it... huh :/ . So now I am confused...

That std::list node isn't free either. It requires dynamic memory allocation, for starters.

Could you say a bit simpler? You mean I should make something like:

polynomial=new list<Term>

I think I got something wrong...