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羅庚 發問於 科學及數學數學 · 5 年前

Remainder Theorem

When a polynomial P(x) is divided by x+1 and x+2 , the remainders are -7 and -25 respectively. Find the remainder when P(x) is divided by (x+1)(x+2).

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  • 5 年前
    最愛解答

    學校嘅做法:Let P(x)=(x+1)(x+2)Q(x)+ax+b, Put x=-1, P(-1)=-a+b=-7==> a-b=7 ⋯⋯⋯⋯ (1)Put x=-2,P(-2)=-2a+b=-25==> 2a-b=25 ⋯⋯⋯ (2)Solve (1), (2), get,a=18,b=11∴ when P(x) is divided by (x+1)(x+2), the remainder is (18x + 11).

    坊間做法:Let P(x)=(x+1)(x+2)Q(x)+c(x+1)-7, Put x=-2,P(-2)=-a-7=-25∴ a=1818(x+1)-7=18x+11∴ when P(x) is divided by (x+1)(x+2), the remainder is (18x + 11).

    2015-02-24 09:28:42 補充:

    Sooty, 坊間嘅做法裡面嘅 "c" 打錯咗,係 "a"。

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