Answer
Not correct factorization
Correct: $(x+1)^2$
Work Step by Step
We graph the polynomial functions:
$$\begin{align*}
p_1(x)&=(x-3)^2+8(x-3)+16\\
p_2(x)&=(x-1)^2.
\end{align*}$$
Because the two graphs do not coincide, this means that the polynomial $p_1(x)=(x-3)^2+8(x-3)+16$ was not factored correctly.
Factor the polynomial $p_1(x)$ correctly:
$$\begin{align*}
p_1(x)&=(x-3)^2+8(x-3)+16\\
&=((x-3)+4)^2\\
&=(x+1)^2.
\end{align*}$$
We draw $p_2(x)=(x+1)^2$ and notice that now the two graphs coincide.