Jika f(x) dibagi x2 – 2x – 8 sisa x + 4. Jika dibagi x2 – 5x + 6 sisa x – 6. Apabila dibagi x2 – 6x + 8 sisanya

Diket.

f(x) = (x²-2x-8).P(x) + (x+4)

= (x-4)(x+2).P(x) + (x+4)

f(4) = 4+4 = 8

f(-2) = -2+4 = 2

f(x) = (x²-5x+6).Q(x) + (x-6)

= (x-2)(x-3).Q(x) + (x-6)

f(2) = 2-6 = -4

f(3) = 3-6 = -3

Dit.

S(x) dari f(x)= (x²-6x+8).H(x) + S(x)

Dijawab:

Misalkan S(x) = ax+b

f(x) = (x²-6x+8).H(x) + S(x)

= (x-2)(x-4).H(x) + ax+b

f(2) = 2a+b

-4 = 2a+b ⇔ 2a+b = -4 ….. (1)

f(4) = 4a+b

8 = 4a+b ⇔ 4a+b = 8 ….. (2)

2a+b = -4

4a+b = 8 –

-2a = -12

a = 6

2a+b = -4

2(6)+b = -4

12 + b = -4

b = -4-12 = -16

Jadi sisa pembagiannya adalah

⇔ S(x)= ax+b

= 6x-16