Also : in general, a polynomial of degree $\displaystyle n$ has at most $\displaystyle n$ roots $\displaystyle \mod p$. In this case, we know $\displaystyle \pm 1$ are two roots, so there can't be any others.
Also : in general, a polynomial of degree $\displaystyle n$ has at most $\displaystyle n$ roots $\displaystyle \mod p$. In this case, we know $\displaystyle \pm 1$ are two roots, so there can't be any others.