Jika R(x) dibagi x^2-3 sisanya 2x+1 dan jika dibagi x^2+3x sisanya 3x .tentukan sisa pembagian R(x) oleh x^2-9

jawab

x² + 3x = 0, sisa s(x) = 2x+ 1
x(x+3) = 0
x  = 0 → s(0) = 1
x = -3 → s(-3) = 2(-3)+1 = -5

x² - 3x = 0 , sisa  s(x) = 3x
x(x-3) = 0
x = 0 , s(0)= 0
x = 3 , s(3) = 3(3) = 9

x² - 9 = 0 , sisa s(x) = ax +b
(x-3)(x+3) = 0
x = 3 , s(3) = 3a + b = 0
x = - 3, s(-3) =-3a + b = 0

3a + b = 0
-3a + b = 0 ] (+)
2b = 0
b = 0
3a + b = 0
3a = 0
a  = 0
s(x) = ax + b → s(x) = 0
R(x) dibagi (x² -9) , sisa = 0
(habis dibagi)