x^2-x-2 =(x-2)(x+1)
f(x) = p(x) .(x^2-x-2) + (-x-5)
f(2) = -2 -5 = -7
f(-1) = 1-5 = -4
x^2-5x+6 =(x-2)(x-3)
f(x) = m(x) .(x^2-5x+6) + (2x+1)
f(2) = 2(2) +1 =5
f(3) = 2(3) +1 = 7
x^2-2x-3 = (x-3)(x+1)
当f(x)被x^2-2x-3除的馀式 = ax+b
f(x) = n(x) .(x^2-2x-3) + (ax+b)
f(3) = 3a+b = 7 (1)
f (-1) = -a+b=-4 (2)
(1)-(2)
4a=11
a=11/4
from (1)
3a+b = 7
33/4+b=7
b= -5/4
ie
f(x)被x^2-2x-3除的馀式 = (11/4)x -5/4
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