f.4 MATHS

First of all, if the polynomial is divided by a quadratic factor, the remainder must be a linear polynomial or a constant.
So to speak, let Px + Q be the remainder where P and Q are constants.
Then, from the given:
f(5) = 9 and f(-2) = -5
So from these results, we can see that:
f(x) = (x-5)(x+2)Q(x) + (Px + Q) where Q(x) is the quotient polynomial.
Put x = 5:
f(5) = 5P + Q
5P + Q = 9 .... (1)
Put x = -2:
f(-2) = -2P + Q
-2P + Q = -5 ....(2)
Solving (1) and (2), we have:
P = 2 and Q = -1
Therefore, the remainder when f(x) is divided by (x-5)(x+2) is 2x - 1.

上面的人已回答得很好，我無話可說！

我唔肯定有無計錯...因為２年無掂過希望無教錯你...........錯左唔好見怪><"

因為f(x) 除 x-5 係=9, 同時 f(x) 除 x+2 係=-5
咁你條式就係：： f(x) = ９／(ｘ-５) = -５／(ｘ+２)
計法如下．．．

f(x) = ９／(ｘ-５) = -５／(ｘ+２)

　 　 　 ９(ｘ+２ = -５(ｘ-５)
　 　 ９ｘ + １８ = -５ｘ+２５
　 　 ９ｘ + ５ｘ = ２５ - １８
　 　 　　１４ｘ = ７
　　 　　ｘ = 0.5

∵ｆ（ｘ）＝ｆ（0.5）
∴　　　ｘ＝　0.5

∴ 　f(x) = (ｘ-５)(ｘ+２)
　ｆ(0.5) = [(0.5)-５][(0.5)+２]
　　 　 = (-4.5)(2.5)
　 　 　 = -11.25 // <~ 答案


希望真係幫到你 -.-"