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急等! 余式定理一题
若f(x)=x³-2x²-x+2,且g(x)=f{f(x)},求g(x)被x-1除的余式
人气:107 ℃ 时间:2020-05-22 22:08:05
解答
f(x)=x³-2x²-x+2
f(x)=(x-2)x²-(x-2)
f(x)=(x-2)(x+1)(x-1)
所以有f(x)/(x-1)余式为0
于是:
g(x)/(x-1)=f{f(x)}/(x-1)
=[f(x)³-2f(x)²-f(x)+2]/(x-1)
=[f(x)³-2f(x)²-f(x)]/(x-1)+2/(x-1)
所以:g(x)被x-1除的余式=2
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