✨ 最佳解答 ✨
可假設f(x)= a(x-1)(x-2)(x-3)+g(x)
f(1)=g(1)=1,
f(2)=g(2)=2,
f(3)=g(3)=5,
將g(x)化簡⥤g(x)=X²-2X+2
(A) g(0)=2...❌
(B)f(5)=a(5-1)(5-2)(5-3)+g(5)...❌
(C)f(4)= a(4-1)(4-2)(4-3)+g(4),a無法求得則f(4)無法求得...❌
(D)g(x)=X²-2X+2=(x-1)(x-2)×1+x
f(x)= a(x-1)(x-2)(x-3)+(x-1)(x-2)×1+x
⥤餘式 = x...⭕️
(E)f(x)= a(x-1)(x-2)(x-3)+g(x)
⥤餘式 = g(x)...⭕️
謝謝大神~~