已知一多項式f(x)被x^4-1除所得餘式是2x^3-5x+7. 若f(x)被x^2-1除所得的餘式是r(x),求r(-2) 答案:13?

f(x) = q(x)(x^4-1) + 2x^3-5x+7
      = q(x)(x^2+1)(x^2-1) +2x(x^2-1) - 3x+7
 所以 f(x) 被 x^2-1 除所得餘式是
   r(x) = -3x+7
∴ r(-2) = -3(-2)+7 = 13