已知除式g(x)=x2-2x+1,商式Q(x)=x2+2x-1,余式R(x)=-4,求被除式f(x).

问题描述:

已知除式g(x)=x2-2x+1,商式Q(x)=x2+2x-1,余式R(x)=-4,求被除式f(x).

被除式f(x)=g(x)×Q(x)+R(x)
=(x2-2x+1)(x2+2x-1)-4
=x4-(2x-1)2-4
=x4-4x2+4x-1-4
=x4-4x2+4x-5.