## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$(x-1)(x+1)(x^2-x+1)$
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 $(x+y)^3=(x+y)(x^2-xy+y^2)$: $$(x-1)(x^3+1)=(x-1)(x+1)(x^2-x+1) .$$