Question

求这题做法要过程

Answer 1

由已知 f(x)
= (x^2+x-6)g(x)+x+2 = (x-2)(x+3)g(x)+x+2
= (x^2-x-2)h(x)+2x-1=(x-2)(x+1)h(x)+2x-1
所以：f(-3) = -1; f(-1) = -3
设r(x) = a x + b; -1=r(-3)=-3a+b; -3=-a+b; => a=-1, b=-4, r(x)=-x-4 为所求余式

Answer 2

f(x) = q(x) .(x^2+x-6) +(x+2)
f(x) = q(x) .(x+3)(x-2) +(x+2) (1)
-------------------
f(x) = g(x) .(x^2-x-2) +(2x-1)
f(x) = g(x) .(x-2)(x+1) +(2x-1) (2)
(1)
from (1) , x=-3
f(-3) = -3+2 = -1
(2)
from (2) , x=-1
f(-1) = -2-1 = -3
(3)
x^2+4x+3 = (x+1)(x+3)
f(x) =m(x).(x+1)(x+3) + ax+b

f(-1) = -a+b = -3 (3)
f(-3) = -3a+b = -1 (4)
(3)-(4)
2a = -2
a=-1
from (3)
1+b=-3
b=-4
f(x) 除以 （x^2+4x+3） 余数 = -x-4