因式分解x^3-2x^2+1

题目

因式分解x^3-2x^2+1

答案

x^3-2x^2+1
=x³-x²-x²+1
=x²(x-1)-(x-1)(x+1)
=(x-1)(x²-x-1)
或者继续分解
x^3-2x^2+1
=x³-1-2x²+2
=(x-1)(x²+x+1)-2(x+1)(x-1)
=(x-1)[(x²+x+1)-2(x+1)]
=(x-1)(x²-x-1)
=(x-1)[x-(1＋√5)/2][x-(1-√5)/2]
-----------------------------------
如有疑问欢迎追问!
满意请点击右上方【选为满意回答】按钮