Question

1. Suku banyak P(x) = x^3 - 2x^2 + ax + b dibagi x^2 - 2x - 3 sisanya x - 4. Jika suku banyak P(x) dibagi x + 2 sisanya adalah?
2. Suku banyak f(x) dibagi oleh (x - 2) sisanya 11, dan dibagi (x + 1) bersisa 5. Apabila f(x) dibagi (x^2 - x - 2) sisanya adalah?
Tolong yaaah

Answer 1

1. P(x) = x³ - 2x² + ax + b dibagi oleh (x + 1)(x - 3) sisanya x - 4
P(-1) = -1 - 4 = -5
(-1)³ - 2(-1)² + a(-1) + b = -5
-1 - 2 - a + b = -5
a - b = 2 ...(1)

P(3) = 3 - 4 = -1
27 - 18 + 3a + b = -1
3a + b = -10 ...(2)

eliminasi (1) dan (2) maka:
a - b = 2
3a + b = - 10
___________ +
4a = -8
a = -2
b = -6

2. misal sisanya ax + b
f(2) = 11
2a + b = 11
f(-1) = 5
-a + b = 5
eliminasi:
2a + b = 11
-a + b = 5
__________ -
3a = 6
a = 2
b = 7
sisa = 2x = 7

semoga membantu :)