Question

多项式p（x）被x2+1除后余式为2x-3,并且p（0）=0,那么p（x）被x（x2+1）除后余式是?

Answer 1

p(x)=q(x)*(x²+1)+2x-3

p(0)=q(0)-3=0,所以q(0)=3,所以q(x)=x*r(x)+3.

所以p(x)=(x*r(x)+3)*(x²+1)+2x-3=r(x)*x(x²+1)+3x²+2x

所以被x(x²+1)除后余式是3x²+2x