Question

Jawab pakai cara!!
1. Suku banyak p(x) dibagi x+1 bersisa -3 dan dibagi x-4 bersisa 17. Jika p(x) dibagi x²-3x-4 maka sisanya berapa?
a. 9x - 7
b. 4x + 1
c. 2x + 3
d. x - 4
e. 3x + 2
2. Diketahui (f o g)(x)=6x²-18x+13 , g(x)=3x²-9x+1 maka nilai f(-½)?
a. -11
b. -8
c. 1
d. 7
e. 10

Answer 1

1) (B)
dibagi (x+1) sisa -3 --> f(-1)= -3
dibagi (x-4) sisa 17 --> f(4) = 17
dibagi x²-3x-4 sisa s(x)= ax +b
x²-3x-4 = 0
(x-4)(x+1) = 0--> x = 4 ataux = -1
s(4) = f(4) --> 4a+ b= 17
s(-1)= f(-1) --> -a + b = -3
kurangkan --> 5a = 20 --> a= 4  dan b = -3 + a = 1
s(x)= 4x + 1

2)(E)
fog(x) = 6x² -18x + 13 , g(x) = 3x² - 9x + 1
f{g(x)} = 6x²- 18x + 13
f(3x² -9x +1) = 6x² - 18x + 13 = 2(3x²-9x+1) + 11
f(-1/2) = 2(-1/2) + 11 
f(-1/2) = 10