你好:
因为除数含有(x-2),因此被除数进行带有(x-2)因子的因式分解
被除数:2x^3-6x^2+3x+5
=2x^2*(x-2)-2x*(x-2)-(x-2)+3
=(x-2)(2x^2-2x-1)+3
=(x-2)*[2x(x-2)+2(x-2)+3]+3
=(x-2)*[(x-2)*(2x+2)+3]+3
=(x-2)^2*2(x+1)+3(x-2)+3
=(x-2)^2*2(x+1)+3x-3
所以:
(2x^3-6x^2+3x+5)/(x-2)^2
=[(x-2)^2*2(x+1)+(3x-3)]/(x-2)^2
=(2x+2) 余(3x-3)
希望对你有帮助!