S.4 maths
2010-08-19 5:34 am
When a polynomial P(x) is divided by x-2, the remainder is 3. When it is divided by x-3, the remainder is 2. find the remainder when P(x) is divided by (x-2)(x-3).
回答 (1)
2010-08-19 6:14 am
✔ 最佳答案
Since when a polynomial P(x) is divided by x-2, the remainder is 3 , we letP(x) = Q(x) * (x - 2)(x - 3) + k(x - 2) + 3When it is divided by x-3, the remainder is 2 , by remainder theorem ,P(3) = 20 + k(3 - 2) + 3 = 2k = - 1SoP(x) = Q(x) * (x - 2)(x - 3) - (x - 2) + 3when P(x) is divided by (x-2)(x-3). , the remainder is - (x - 2) + 3= - x + 5
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