Question

多项式(x^2+4x+5)^3除以x^2+3x+7所得之余式

Answer 1

(x^2+4x+5)^3

=[(x^2+3x+7)+(x-2)]^3

=(x^2+3x+7)^3+3(x^2+3x+7)^2(x-2)+3(x^2+3x+7)(x-2)^2+(x-2)

=(x^2+3x+7)[(x^2+3x+7)^2+3(x^2+3x+7)(x-2)+3(x-2)^2]+(x-2)

余式为(x-2)