Answer
$(x+4)(x+1)$
Work Step by Step
The given expression has $a=1$, $b=5$, and $c=4$
Look for factors of $c=4$ whose sum is equal to the coefficient of the middle term (which is $b=5$). The factors are $4$ and $1$.
Rewrite the middle term using the factors found above (rewrite $5x$ as $4x+x$).
$x^2+5x+4=x^2+4x+x+4$
Group the terms.
$=(x^2+4x)+(x+4)$
Factor out the GCF in each group.
$=x(x+4)+1(x+4)$
Factor out $(x+4)$.
$=(x+4)(x+1)$
Hence, the completely factored form of the given expression is $(x+4)(x+1)$.
