how do you factorize x^3-x^2+1

Question

I need help to factor this problem x^3-x^2+1

Answer 1

Scott is right that this polynomial cannot be factored, but I will explain why this is the case.  According the rational-root theorem, the possible roots are -1 and 1. 

 

This means that one of these factors can be either (x + 1) or (x - 1).  If we divide the given polynomial by one of these possible factors, then remainder must be zero.  But for each of these factors, the remainder is never zero.

 

 

In addition to this, if we graph this polynomial on a graphing calculator, we will see the x-intercept is an irrational number.

Answer 2

X³-x²+1 cannot be factored.