Suatu suku banyak f(x) dibagi x-1 siaanya 6 dan dibagi x+3 sisanya -2. Bila fx dibagi x2+2x-3

f(1) = 6
f(-3) = -2

misal s(x) = ax + b

f(x) = (x^2 + 2x - 3)×H(x) + S(x)
f(x) = (x - 1)(x + 3)×H(x) + ax + b
f(1) = (1-1)(1+3)×H(1) + a×1 + b
f(1) = 0(4)×H(1) + a + b
6 = 0 + a + b
a + b = 6 ...... (1)

f(-3) = (-3-1)(-3+3)×H(-3) + a×(-3) + b
f(-3) = (-4)(0)×H(-3) + (-3a) + b
-2 = 0 - 3a + b
3a - b = 2 .......(2)

dari (1) dan (2)

a + b = 6
3a - b = 2
________ +
4a = 8
a = 2


b = 6 - a
b = 6 - 2
b = 4

s(x) = 2x + 4