$29 \cdot 56$ The remainder of the polynomial $x^{12}-x^{6}+1$ divided by $x^{2}-1$ is
(A) 1 .
(B) -1 .
(C) $x-1$.
(D) $x+1$.
(China Junior High School Mathematics League, 1993)
[Solution] From $x^{12}-x^{6}+1=x^{6}\left(x^{6}-1\right)+1$ $=x^{6}\left[\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)\right]+1$, we know that the remainder when $x^{12}-x^{6}+1$ is divided by $x^{2}-1$ is 1. Therefore, the answer is $(A)$.