1. The remainder of the polynomial $x^{12}-x^{6}+1$ divided by $x^{2}-1$ is
(A) 1 ;
(B) -1 ;
(C) $x-1$;
(D) $x+1$.
1. (A)
$$
\begin{aligned}
\because \quad x^{12}-x^{6}+1 & =x^{6}\left(x^{6}-1\right)+1 \\
& =x^{6}\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)+1,
\end{aligned}
$$
$\therefore$ the remainder is 1.