Answer
$(x-1)(x+1)(x^2-x+1)$
Work Step by Step
We factor by grouping as follows
$$
x^4 - x^3 + x - 1= x^3(x-1)+(x-1)
.$$
Now, factoring $x-1$ out, we have
$$
x^3(x-1)+(x-1) =(x-1)(x^3+1)
.$$
Finally, we apply the formula $(x+y)^3=(x+y)(x^2-xy+y^2)$:
$$
(x-1)(x^3+1)=(x-1)(x+1)(x^2-x+1)
.$$
