Question

利用竖式求：x的4次方-3x的3次方-2x的平方+5x+3除以x-1后的商式和余式

Answer 1

x的4次方-3x的3次方-2x的平方+5x+3

=x^3(x-1)-2x^3-2x^2+5x+3

=x^3(x-1)-2x^2(x-1)-4x^2+5x+3

=x^3(x-1)-2x^2(x-1)-4x(x-1)+x+3

=x^3(x-1)-2x^2(x-1)-4x(x-1)+(x-1)+4

=(x^3-2x^2-4x+1)(x-1)+4

商式:x^3-2x^2-4x+1

余式:4