证明6x^5+11x^4+5x^3+5x^2-x-6能被x^2+1整除?

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/19 02:54:58

证明6x^5+11x^4+5x^3+5x^2-x-6能被x^2+1整除?
提示：判断6x^5+11x^4+5x^3+5x^2-x-6是否含因式（x+i)(x-i)

6x^5+11x^4+5x^3+5x^2-x-6
=6x^5+6x^3+11x^4-x^3+5x^2-x-6
=6x^3(x^2+1)+11x^4+11x^2-x^3-6x^2-x-6
=6x^3(x^2+1)+11x^2(x^2+1)-(x^3+x)-(6x^2+6)
=6x^3(x^2+1)+11x^2(x^2+1)-x(x^2+1)-6(x^2+1)
所以,得证.

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