x^5-x^3+x^2-1 因式分解

分类: 作业答案 • 2023-01-20 00:29:13

问题描述：

x^5-x^3+x^2-1 因式分解

答

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