Show that has four zeros in .
, by the factor theorem, -1 and -2 are zeros of the poly.
However, -2 = 4 and -1 = 5 in . But what are the other two?
Thanks.
I just want to mention the interesting fact that even though the polynomial is of degree 2 it has 4 zeros. That might seem impossible but there is a reason for it. That theorem (about polynomials having at most the number of zeros of its degree) is only for fields (or when the division algorithm works). But Z_6 is not a field so it is not supprising why it fails.