✔ 最佳答案
設f(x) = x^3 + cx^2 + 3x + d
根據餘式定理，f(2) = -14
(2)^3 + c(2)^2 + 3(2) + d = -14
4c + d = -28 ... (1)
f(-1) = -17
(-1)^3 + c(-1)^2 + 3(-1) + d = -17
c + d = -13 ... (2)
得出c = -5，d = -8
1. 設f(x) = 3x^3 + 2x^2 + cx + d
根據餘式定理，f(1/2) = -17/8
3(1/2)^3 + 2(1/2)^2 + c(1/2) + d = -17/8
c/2 + d = -3 ... (1)
f(-2) = -44
3(-2)^3 + 2(-2)^2 + c(-2) + d = -44
-2c + d = -28 ... (2)
求出c = 10，d = -8
2. f(x) = (2x^2 - x + 3)(8x - 3) + 4
根據餘式定理，f(x)除1 - 4x的餘數
= f(1/4)
= [2(1/4)^2 - (1/4) + 3][8(1/4) - 3] + 4
= 9/8
3. 設f(x) = px^2 + 2x + 5
f(2) = f(-1/2)
p(2)^2 + 2(2) + 5 = p(-1/2)^2 + 2(-1/2) + 5
p = 4/3
