AMC 12B 2021 Spring Problem 20

Let Q(z) and R(z) be the unique polynomials such that

z^{2021}+1=\left(z^{2}+z+1\right) Q(z)+R(z)

and the degree of R is less than 2 . What is R(z) ?

Answer Choices
A. -z
B. -1
C. 2021
D. z+1
E. 2 z+1