Answer to Question #192579 in Abstract Algebra for Neena peter

Question

Which of the following is a zero divisor in the polynomial ring z12[x]. A)1+x, B)2+x, C)3+2x,D) 4+2x

Answer 1

Solution:

In $Z_{12}$, the zero divisors are 2, 3, 4, 6, 8, 9, 10.

So, in $Z_{12}[x]$ , zero divisors are $2+x, 3+x, 4+x,6+x,8+x,9+x,10+x$

Thus, only $2+x$ is correct out of the given options.

Hence, option B).