Answer
$x^{5}+x^{4}+x+1=(x^{4}+1)(x+1)$
Work Step by Step
$x^{5}+x^{4}+x+1$
Group the first two terms together. Do the same with the last to terms:
$x^{5}+x^{4}+x+1=(x^{5}+x^{4})+(x+1)=...$
Take out common factor $x^{4}$ from the first parentheses:
$...=x^{4}(x+1)+(x+1)=...$
Finally, take out common factor $(x+1)$:
$...=(x^{4}+1)(x+1)$
