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F.4 maths

發問:

When a certain polynomial f(x) is divided by (x-1)(3x+2), the remainder is px+q. When f(x) is divided by x-1, the remainder is -4; when f(x) is divided by 3x+2,the remainder is 6.Find the values of p and q.

最佳解答:

Let f(x) = (x - 1)(3x +2)Q(x) + (px + q) By remainder theorem, f(1)= -4 i.e. (1 - 1)[3(1) + 2]Q(1)+ (p + q) = -4 p + q = -4 ─── (1) By remainder theorem,f(-2/3) = 6 i.e. [1 – (-2/3)][3(-2/3)+ 2]Q(-2/3) + [p(-2/3) + q] = 6 -2p + 3q = 18 ───(2) (1) X 2 + (2): 5q = 10 q = 2 p = -6

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