Question

Which of the following polynomial is irreducible over $Z_{3}$, a field modulo 3?

• A. $x^{2} + 2$
• B. $2x + 1$
• C. $x^{2} + 1$
• D. $x - 1$

Hint:

To check irreducibility of $x^2 + k$ over $Z_p$, check if $-k$ is a quadratic residue modulo $p$.

Answer 1

The Correct Option is C