Question

Suku banyak k(x) dan m(x) jika dibagi x² - 6x + 8 masing-masing sisanya adalah x + 9 dan 2x - 3. Diketahui suku banyak g(x) memenuhi g(x) = k(x).m(x). sisa pembagian g(x) oleh x² - 6x + 8 adalah?

Answer 1

(x^2 - 6x + 8) = (x - 4)(x - 2) => x = 4 dan x = 2
k(x) : (x^2 - 6x + 8) bersisa x + 9
=> k(4) = 4 + 9 = 13
=> k(2) = 2 + 9 = 11
m(x) : (x^2 - 6x + 8) bersisa 2x - 3
=> m(4) = 2(4) - 3 = 5
=> m(2) = 2(2) - 3 = 1
g(x) = k(x) . m(x)
g(x) : (x^2 - 6x + 8) bersisa ax + b
g(4) = k(4).m(4) = 13.5 = 65
g(2) = k(2).m(2) = 11.1 = 11

g(4) = 4a + b = 65
g(2) = 2a + b = 11
------------------------- -
........... 2a = 54 => a = 27
2a + b = 11 => b = 11 - 2(27) = -43
Jadi sisanya ax + b = 27x - 43