多项式f(x)以x-1除之余式为9,以x-2除之余式为16,求f(x)除以(x-1)(x-2)的余式.
问题描述:
多项式f(x)以x-1除之余式为9,以x-2除之余式为16,求f(x)除以(x-1)(x-2)的余式.
答
根据题意得:∵f(x)=g(x)(x-1)+9①,f(x)=h(x)(x-2)+16②,∴②×(x-1)-①×(x-2)得:[(x-1)-(x-2)]f(x)=[h(x)-g(x)](x-1)(x-2)+16(x-1)-9(x-2)=[h(x)-g(x)](x-1)(x-2)+7...