Answer
$(x-1)(x+1)(x^2-x+1)$
Work Step by Step
Group the first two terms together and group the last two terms together.
$x^4-x^3+x-1=(x^4-x^3)+(x-1)$
Factor out the GCF in each group.
$=x^3(x-1)+1(x-1)$
Factor out $(x-1)$.
$=(x-1)(x^3+1)$
$=(x-1)(x^3+1^3)$
Use special formula $a^3+b^3=(a+b)(a^2-ab+b^2)$ where $a=x$ and $b=1$.
$=(x-1)[(x+1)(x^2-x(1)+1^2)]$
$=(x-1)(x+1)(x^2-x+1)$
Hence, the completely factored form of the given expression is $(x+1)(x-1)(x^2-x+1)$.
