Question

Jika x^3 – 1 ≡ (x−2) (x −3) (x + a) + bx + c maka nilai dari b − c adalah

Answer 1

F(x) = g(x)h(x) + s(x)
x^3 - 1 = (x - 2)(x - 3)(x + a) + bx + c
f(2) = g(2)h(2) + s(2)
2^3 - 1 = (2 - 2)(2 - 3)(2 + a) + 2b + c
8 - 1 = 2b + c
7 = 2b + c

f(x) = g(x)h(x) + s(x)
x^3 - 1 = (x - 2)(x - 3)(x + a) + bx + c
f(3) = g(3)h(3) + s(3)
3^3 - 1 = (3 - 2)(3 - 3)(3 + a) + 3b + c
27 - 1 = 3b + c
26 = 3b + c

3b + c = 26
2b + c = 7
__________-
b = 19

2(19) + c = 7
38 + c = 7
c = 7 - 38
c = -31

b - c = 19 - (-31) = 50