补充作业2:设f(x),(x)∈K],令 92={u(x)f(x)+u(x)g(x)u(x),v(x)∈K[]} 求证:(1)若a(x),b(x)∈92,则a(x)±b(x)∈92; (2)若a(x)∈9,则对任意h(x)∈K[X],有a(x)h(x)∈9 (3)存在首项系数为1的d(x)∈9,使得对va(x)∈9,有d(x)a(x); 4)d(x)=(f(x),g(x) 思考题:P1945,6,7 选做:设a,b,c两两互异,用x-a,x-b,x-c除∫(x)的余式分别为r,s,t 试求用(x-a)(x-b)(x-c)除∫(x)的余式5 2: i f(x), g(x) ∈ K[x], O Ω = {u(x)f(x) + v(x)g(x)|u(x), v(x) ∈ K[x]}. ℄) (1) e a(x), b(x) ∈ Ω, # a(x) ± b(x) ∈ Ω; (2) e a(x) ∈ Ω, #&a h(x) ∈ K[X],  a(x)h(x) ∈ Ω; (3) "p
r~ 1 ! d(x) ∈ Ω, l & ∀a(x) ∈ Ω,  d(x)|a(x); (4) d(x) = (f(x), g(x)). tFy P194 5, 6, 7. 4i a, b, c LL:￾ x − a, x − b, x − c  f(x) !m- ~ r, s, t. o℄ (x − a)(x − b)(x − c)  f(x) !m
7