1.jika f(x) dibagi oleh x-1 sisanya 4 dibagi x+1 sisanya -3,dan dibagi x-2 sisanya 2 tentukan sisanya jika f(x) dibagi (x-1)(x+1)(x-2)? 2.JIka f(x) dibagi oleh

jawab
1.
di bagi (x-1) sisa 4 → f(1) = 4
dibagi (x+1) sisa -3 → f(-1) = -3
dibagi (x-2) sisa 2  → f(2) = 2
dibagi (x-1)(x+1)(x-2)  sisa  f(x) = ax² + bx + c
f(1) = 4 → a + b + c = 4
f(-1) = -3 → a - b + c = -3
f(2) = 2 → 4a + 2b + c = 2

a + b + c = 4
a - b + c = - 3 ||(-)
2b = 7 → b = 7/2

a + b + c = 4
a - b+ c = - 3 ||(+)
2(a+c) = 1
a + c = 1

a + b + c = 4 || kali 2
4a + 2b + c = 2

2a + 2b + 2c = 8
4a + 2b  + c = 2 ||(-)
-2a  + c =  6

a + c = 1
-2a +c = 6 || (-)
3a = - 5
a = - 5/3
c = 1- a = 1 - 5/3 =  -2/3

sisa = -5/3 x² + 7/2 x - 2/3
sisa = 1/6 (-10 x² + 21 x - 4)

2. f(x) = ax + b
f(1) =  4
f(-1)  = -3
(1 -(-1)) a = 4- (-3)
2a = 7
a= 7/2
b = 4 - a
b = 4 - 7/2 = 1/2
f(x) = 7/2 x + 1/2
f(x) = 1/2 (7x + 1)