## Precalculus: Mathematics for Calculus, 7th Edition

$5x^{3}+x^{2}+5x+1=(x^{2}+1)(5x+1)$
$5x^{3}+x^{2}+5x+1$ 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 $(5x+1)$: $...=(x^{2}+1)(5x+1)$