Question

Diberikan polinomial p(x) yang jika dibagi oleh (x2-x-6) sisanya (3x+2)dan jika dibagi oleh(x-2) sisanya 8.
tentukan sisa pembagian polinomial p(x) tersebut oleh (x2-4)

Answer 1

1. P(x)/(x+2)(x-3) = 3x+2
   s(x) = p(-2) = 3(-2)+2 = -4
   s(x) = p(3) = 3(3)+2 = 11

2. p(x)/(x-2) = 8
s(x) = p(2) = 8 

p(x)/(x²-4) = p(x)/(x+2) (x-2)
p(x) = (x+2) (x-3) h(x)+px+q
p(-2) = -2p+q = -2p+q =-4
p(2) = 2p+q = 2p+q = 8

-2p+q = -4
2p+q = 8 -
-4p = -12
p = 3

2p+q = 8
2(3)+q = 8
6+q = 8
q = 2

jadi, s(x) = 3x+2