Question

Misalkan f(x) = 3x^3 − 9x^2 + 4bx + 18 = (x − 2)g(x) + 2b maka g(−2)

Answer 1

Verified answer

F(x) = 3x^3 - 9x^2 + 4bx + 18 = (x - 2)g(x) + 2b
g(-2) = ......????
x - 2 = 0 => x = 2
Substitusikan x = 2 ke persamaan
3x^3 - 9x^2 + 4bx + 18 = (x - 2)g(x) + 2b
diperoleh persamaan
3(2)^3 - 9(2)^2 + 4b(2) + 18 = (2 - 2)g(2) + 2b
3(8) - 9(4) + 8b + 18 = (0) g(2) + 2b
24 - 36 + 8b +18 = 2b
6 + 8b = 2b
8b - 2b = -6
6b = -6
b = -6/6
b = -1
Sehingga :
3x^3 - 9x^2 + 4(-1)x + 18 = (x -2)g(x) + 2(-1)
3x^3 - 9x^2 - 4x + 18 = (x - 2)g(x) - 2
Substitusikan x = -2
3(-2)^3 - 9(-2)^2 - 4(-2) + 18 = (-2 - 2)g(-2) - 2
3(-8) - 9(4) - (-8) + 18 = -4 g(-2) - 2
-24 -36 + 8 + 18 = -4 g(-2) - 2
-34 = -4 g(-2) - 2
4 g(-2) = -2 + 34
4 g(-2) = 32
g(-2) = 32/4
g(-2) = 8
Jadi nilai g(-2) = 8