Let $a$ and $b$ be integers such that
$$\begin{aligned}& P ( x ) = x ^ { 3 } - a x ^ { 2 } - ( b + 2 ) x + 4 b \\& Q ( x ) = x ^ { 2 } - 2 a x + b\end{aligned}$$
For the polynomials
\begin{itemize}
\item $\mathrm{P} ( - 4 ) = 0$
\item $\mathrm{Q} ( - 4 ) \neq 0$
\end{itemize}
it is known that.\
If the roots of polynomial $\mathbf{Q} ( \mathbf{x} )$ are also roots of polynomial $\mathbf{P} ( \mathbf{x} )$, what is the difference $b - a$?\
A) 8\
B) 9\
C) 11\
D) 13\
E) 14