When a polynomial f(x) is divided by x-5, the remainder is 9; when it is divided by x+2, the remainder is -5. Find the remainder when f(x) is divided by (x-5)(x+2).
Please show your steps clearly.
Remainder theorem
2013-01-17 3:40 am
回答 (1)
2013-01-17 4:19 am
✔ 最佳答案
Let f(x) = P(x)(x - 5) + 9 = Q(x)(x + 2) - 5Let f(x) = T(x)(x - 5)(x + 2) + ax + b
Sub x = 5, 5a + b = 9
Sub. x = -2, -2a + b = -5
Solve it, a = 2, b = -1
So, the remainder is 2x - 1
收錄日期: 2021-04-13 19:16:09
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