“X的3次方减X的平方减X加1”分解因式是多少？

分解因式,就可以用初中常用代方程找公因式.即先令此式等于零,后求其解,则可化为(X-*)(X-&)...的标准分解因式模式.像此类简单多次多项式,不好直接求其解,便可先带入简单数字(如1,-1,2,-2,3,-3)使该多项式等于零,则可判定必含(X-$)因式($指上述满足条件的"简单数字"),而后便可一步一步化归化简了.PS:答案为(X+1)(X-1)^2

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

(x+1)(x-1)^2

x³-x²-x+1
=x²(x-1)-(x-1)
=(x-1)(x²-1)
=(x-1)(x+1)(x-1)
=(x+1)(x-1)²