Question

Suku banyak f(x) dibagi (x+1) sisa -2 dan dibagi (x-3) sisa 7,suku banyak g(x) dibagi (x+1) sisa 3 dan dibagi (x-3) sisa 2 .diketahui h(x) = f(x) . g(x) .jika h(x) dibagi x2 - 2x - 3, sisanya adalah....

Answer 1

Misalkan
s(x) = ax + b
f(x) dibagi x+1 sisa -2 berarti
f(-1) = -2
f(3) = 7

g(x) dibagi x+1 sisa 3
g(-1) = 3
g(3) = 2

h(x) = f(x).g(x)
dibagi x²-2x-3 =( x-3)(x+1)
h(3) = f(3).g(3)
h(3) = 7.2 = 14
h(3) = s(3) = 3a + b = 14... pers 1)
h(-1) = f(-1).g(-1)
h(-1) = -2.3 = -6
h(-1) = s(-1) = -a + b = -6 ..... pers 2)

eliminasi pers 1) dan ke 2)

3a + b = 14
-a + b = -6
----------------- -
4a = 20
a = 5
b = -6+a
b = -6+5
b= -1
jdi..
s(x) = 5x - 1