  Self-Reciprocal Irreducible Monic (SRIM) and Self-Conjugate-Reciprocal
Irreducible Monic (SRCIM) factors of $x^n-1$ over finite fields have become of
interest due to their rich algebraic structures and wide applications. In this
paper, these notions are extended to factors of $x^n+ 1$ over finite fields.
Characterization and enumeration of SRIM and SCRIM factors of $x^n+1$ over
finite fields are established. Simplification and recessive formulas for the
number of such factors are given. Finally, applications in the studied of
complementary negacyclic codes are discussed.
