F4 Maths question!

When a polynomial f(x) is divided by x-5,the remaider is 9.When it is divided by x+2,the remainder is -5.Find the remainder when f(x) divided by (x+2)(x-5)

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  • 9 年前
    最愛解答

    Let Q(x) * (x-5)(x+2) + k(x-5) + 9 be f(x) :f(-2) = 0 + k(-2-5) + 9 = - 5-7k = - 5 - 9k = 2So f(x) = Q(x) * (x-5)(x+2) + 2(x-5) + 9= Q(x) * (x-5)(x+2) + 2x - 1

    The remainder = 2x - 1

    Alternatively :

    Let ax + b be the remainder :

    By remainder theorem :

    f(5) = a(5) + b = 9

    {

    f(-2) = a(-2) + b = -5

    Slove it , a = 2 , b = - 1

    The remainder is 2x - 1.

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