when P(x) is divided by (x-1),the remainder is -2 ,When P(x) is divided by(x+1),the remainder is -8.

题目

when P(x) is divided by (x-1),the remainder is -2 ,When P(x) is divided by(x+1),the remainder is -8.Determine remainder when P(x) is divided by x²-1.

答案

设P(x) = C(x) * (x^2-1) + ax + b,(ax+b)为余式.
则由ax+b = a(x-1) + (b+a) 得知 b+a = -2
由ax+b = a(x+1) + (b-a) 得知b-a=-8 所以解得 b=-5,a=3
所以P(x)除以(x^2-1) 剩下 3x-5

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