maths polynomial

Let cx+d be the remainder when P(x)is divided by (x-2)(x-3)
Then P(x)=Q(x)(x-2)(x-3)+ cx+ d where Q(x) is the quotient <<< cx+d 係remainder

when P(x) is divided by x-2
P(2)= 3 ,,,,, 2c+d=3,,,,,,,> (1)
when P(x) is divided by x-3
P(3) =2 ,,,,, 3c+d=2,,,,,,,>(2)

(2)- (1): c= -1
d= 5

SO the remainder is (-x+5)

let左remainder 係 cx+d
首先你要明白 P(X) 可以寫成 quotient 成 dividsor 再+ remainder
有一樣野要注意係 因為 dividsor 係一條二次方程式 (有x二次) 所以 係remainder 到就有一個x <<<<< 呢樣野我唔知y 卡

而後 P(X) 就有一條式表示 根據條式 xc+d 係P(x) 冇論x=咩都係 remainder
根據 題目 given 既detail .. 做左兩條 formula 就可以 找到 c 同 d

Let P(x)= (x-2)(x-3)Q(x)+ax+b, where the remainder is of the form ax+b
Hence, P(2)=3,
∴2a+b=3-----(1),

P(3)=2
∴3a+b=2-----(2).

By solving equation (1) & (2)
a= -1
b=5
i.e. The remainder is -x+5.