1. When P(x) is divided by x-1, the remainder is 3. When divided by x+2, the remainder is 6. When divided by x-3, the remainder is 11.
Find the remainder when P(x) is divided by (x-1)(x+2)(x-3).
F4 Maths Remainder Theorem 5
2009-10-13 6:45 am
回答 (1)
2009-10-13 6:52 am
✔ 最佳答案
Let P(x) = Q(x)(x - 1)(x + 2)(x - 3) + ax^2 +bx + cP(1) = a + b + c = 3 ... (1)
P(-2) = 4a - 2b + c = 6 ... (2)
P(3) = 9a + 3b + c = 11 ... (3)
(2) - (1) => 3a - 3b = 3
a - b = 1 ... (4)
(3) - (2) => 5a + 5b = 5
a + b = 1 ... (5)
(4) + (5) => 2a = 2
a = 1
(4) => b = 0
(1) => c = 2
The remainder is x^2 + 2
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