Answer
$5x^{3}+x^{2}+5x+1=(x^{2}+1)(5x+1)$
Work Step by Step
$5x^{3}+x^{2}+5x+1$
Group the first two terms together. Do the same with the last two terms:
$5x^{3}+x^{2}+5x+1=(5x^{3}+x^{2})+(5x+1)=...$
Take out common factor $x^{2}$ from the first parentheses:
$...=x^{2}(5x+1)+(5x+1)=...$
Finally, take out common factor $(5x+1)$:
$...=(x^{2}+1)(5x+1)$
