Answer
Incorrect factorization
Correct: $(x+2)^2$
Work Step by Step
We graph the polynomial functions:
$$\begin{align*}
p_1(x)&=x^2+4x+4\\
p_2(x)&=(x+4)^2.
\end{align*}$$
Because the two graphs do not coincide, this means that the polynomial $p(x)=x^2+4x+4$ was not factored correctly.
Factor the polynomial $p_1(x)$ correctly:
$$p_1(x)=x^2+4x+4=(x+2)^2.$$
We draw $p_2(x)=(x+2)^2$ and notice that now the two graphs coincide.