Question

Suku banyak (x^3-2x^2+ax+b) dibagi (x^2-2x-3) sisanya (x-4). Nilai (a+b) adalah..

Answer 1

(x²-2x-3) dijabarkan menjadi (x+1)(x-3)

horner
   |1  -2   a   b
-1|v   -1   3   -a-3
________________ +
    1  -3   a+3   b-a-3
f(x) = (x+1) (x²-3x+a+3)+ (b-a-3)

horner 2
    | 1    -3    a+3
3  |  v    3       0
________________+
      1    0        a+3

f(x) = (x+1) [(x-3) (x) + (a+3)] + (b-a-3)
f(x) = (x+1) (x-3) (x) + (x+1) (a+3) +(b-a-3)

s(x) = ax+3x+a+3+b-a-3
x-4 = ax +3x+b
x-3x-4 = ax+b
-2x-4 =ax+b

a= -2    b=-4