Answer
$x^{3}+4x^{2}+x+4=(x^{2}+1)(x+4)$
Work Step by Step
$x^{3}+4x^{2}+x+4$
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 $(x+4)$:
$...=(x^{2}+1)(x+4)$
