Question

余数定理例题

余数定理一道题
多项式除（x-3）余5,除（x+1)余7,除(x^2-2x-3)余几?
我没学过余数定理,能不能通俗的讲讲,不要百度的!

Answer 1

多项式f(x)
多项式除（x-3）余5
f(x) = q(x) .(x-3) + 5
f(3) =5
多项式除(x+1)余7
f(x) = p(x).(x+1) +7
f(-1) =7
f(x) = r(x)(x^2-2x-3) + (ax+b)
f(3) = 3a+b = 5 (1)
f(-1) = -a+b = 7 (2)
(1)-(2)
4a=-2
a=-1/2
from (1)
-3/2 +b =5
b = 13/2
ie
多项式f(x) 除(x^2-2x-3)余 -(1/2)x +13/2