polynomial

👨🏻‍🏫 學術台數學

[匿名]

2010-02-21 5:10 am

when a polynomial f(x) is divided by x+2 and x+3, the remainders are 11 and 6
respectively. find the remainder when f(x) is divided by (x+2)(x+3).

更新1:

Q(x) (x+2)(x+3) + k(x+3) + 6點黎??

更新2:

個remainder點解係k(x+3) + 6

回答 (1)

用戶2053

2010-02-21 5:16 am

✔ 最佳答案

Let f(x) = Q(x) (x+2)(x+3) + k(x+3) + 6
f(-2) = 0 + k(-2+3) + 6 = 11
k + 6 = 11
k = 5
The remainder when f(x) is divided by (x+2)(x+3).
= k(x+3) + 6
= 5(x+3) + 6
= 5x + 21

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