Question

show that x2+x+4 is irreducible over Z11.

Answer 1

Answer on Question #64365 – Math – Abstract Algebra

Question

Show that $x^2 + x + 4$ is irreducible over $\mathbb{Z}_{11}$.

Solution

Since the polynomial has degree 2, it is irreducible over a field if and only if it has no roots in the field. Let's check that:

We used Reducibility Test for Degrees 2 and 3 to prove that the given polynomial is irreducible over the given field.

Answer provided by www.AssignmentExpert.com