## Precalculus: Mathematics for Calculus, 7th Edition

$x^{3}+4x^{2}+x+4=(x^{2}+1)(x+4)$
$x^{3}+4x^{2}+x+4$ Group the first two terms and the last two terms together: $x^{3}+4x^{2}+x+4=(x^{3}+4x^{2})+(x+4)=...$ Take out common factor $x^{2}$ from the first parentheses: $...=x^{2}(x+4)+(x+4)=...$ Now, finish the factoring process by taking out common factor $(x+4)$: $...=(x^{2}+1)(x+4)$