Answer
$(x+ 2)^2$
Work Step by Step
To factor a quadratic polynomial in the form $x^2 + bx + c$, we look at factors of the product of $c$ such that, when added together, equal $b$.
For the equation $x^2 + 4x + 4 = 0$, $c=4$, so look for factors of $4$ that when added together will equal $4$. This means that we need two positive factors. We came up with the following possibilities:
$4=(4)(1)$
$4+1 = 5$
$4=(2)(2)$
$2+2 = 4$
The second pair, $2$ and $2$ is what we are looking for.
This means that the factored form of the trinomial is:
$$(x + 2)(x + 2)$$
The above expression can be rewritten as:
$$(x+ 2)^2$$
