Question

设用 x-1 除f(x)余数为5,用 x+1 除f(x)余数为7，x方-1除f（x）余数等于？

Answer 1

f(x) =q(x)(x-1) +5
f(x) =p(x)(x+1) +7
f(x) =r(x)(x^2-1) + (ax+b)
f(1) =5
a+b =5 (1)
f(-1)=7
-a+b=7 (2)
(1)-(2)
2a=-2
a=-1
from (1)
a+b =5
-1+b=5
b=6
(x^2-1) 除f（x）余数 = -x+6