证明6x^5+11x^4+5x^3+5x^2-x-6能被x^2+1整除?
问题描述：
证明6x^5+11x^4+5x^3+5x^2-x-6能被x^2+1整除?
答
6x^5+11x^4+5x^3+5x^2-x-6=(6x^5+6x^4)+(5x^4+5x^3)+(5x^2-x-6)=6x^4(x+1)+5x^3(x+1)+(5x-6)(x+1)=(x+1)(6x^4+5x^3+5x-6)=(x+1)[(6x^4-6)+(5x^3+5x)]=(x+1)[6(x^2+1)(x^2-1)+5x(x^2+1)]=(x+1)(x^2+1)(6x^2+5x-6)因为...