x5-x4+x3-x2+x-1因式分解

题目

x5-x4+x3-x2+x-1因式分解

答案

x5-x4+x3-x2+x-1
=x4(x-1)+x2(x-1)+(x-1)
=(x-1)(x4+x2+1)
=(x-1)(x4+2x2+1-x2)
=(x-1)[(x2+1)2-x2]
=(x-1)(x2+x-1)(x2-x+1)