# Another way to determine if a polynomial is irreducible over a ring, is to check if the zeros of the polynomial are in the ring, ie, does p have a linear factor.

Another way to determine if a polynomial is irreducible over a ring, is to check if the zeros of the polynomial are in the ring, ie, does p have a linear factor.

"The zeros" are all the zeros?

A linear factor is only one factor?

If a (monic) polynomial over a (commutative) ring (with one) has a linear factor, than it is of course reducible. But the converse is obviously false, e.g. $(x^2+2)^2$ over integers, even over reals, or as is over some finite field...

This looks like homework, please insert the own trials and errors.