suku banyak f(x) dibagi (x-2) sisa 1, dibagi (x+3) sisa -8. Suku banyak g(x) dibagi (x-2) sisa 9, dibagi (x+3) sisa 2. jika h(x) = f(x).g(x), maka sisa pembagia

Materi: Suku banyak

f(x) = (x-2)H(x) + 1 f(2) = 1
f(x) = (x+3)H(x)-8 f(-3)=-8
g(x) = (x-2)H(x)+9 g(2) = 9
g(x) = (x+3)H(x)+2 g(-3) = 2

h(x) = (x+3)(x-2)H(x)+ax+b
h(2) = f(2).g(2) = 9 = 2a+b
h(-3) = f(-3).g(-3) = -16 = -3a+b
Eliminasi b shg diperoleh
25 = 5a, a = 5, akibatnya b = -1
Jadi sisa pembagiannya adalah 5x-1.

f(x) : (x - 2) sisa 1 => f(2) = 1
f(x) : (x + 3) sisa -8 => f(-3) = -8

g(x) : (x - 2) sisa 9 => g(2) = 9
g(x) : (x + 3) sisa 2 => g(-3) = 2

h(x) = f(x) . g(x)
h(2) = f(2) . g(2) = 1 . 9 = 9
h(-3) = f(-3) . g(-3) = -8 . 2 = -16

h(x) : (x^2 + x - 6) misalkan bersisa (ax + b)
x^2 + x - 6 = (x - 2)(x + 3) => x = 2 atau x = -3
h(2) = 2a + b = 9
h(-3) = -3a + b = -16
--------------------------- -
............ 5a = 25 => a = 5

2a + b = 9 => 2(5) + b = 9 => b = -1

Sisa = ax + b = 5x - 1