This has been a huge controversy in the vast world of mathematics. It can be 0 and it can also be 1. That's why mathematicians formally recognize it as an ambiguous number or an indeterminate number. There is no need to be worried or have a fear of this coming up on a standardized test; most test makers avoid asking controversial questions. But if they do ask it, hopefully, there will be an option saying something like indeterminate/ambiguous/undefined.
Basically the remainder theorem links the remainder of division by a binomial with the value of a function at a point while the factor theorem links the factors of polynomial to its zeros
