Answer
$x^{3}+x^{2}+x+1=(x^{2}+1)(x+1)$
Work Step by Step
$x^{3}+x^{2}+x+1$
Group the first two terms together. Do the same with the last two terms:
$x^{3}+x^{2}+x+1=(x^{3}+x^{2})+(x+1)=...$
Take out common factor $x^{2}$ from the first parentheses:
$...=x^{2}(x+1)+(x+1)=...$
Finally, take out common factor $(x+1)$:
$...=(x^{2}+1)(x+1)$
