29 -46 If $f(x)=x^{4}+4 x^{3}+6 p x^{2}+4 q x+r$ can be exactly divided by $g(x)=x^{3}$ $+3 x^{2}+9 x+3$, then the value of $(p+q) r$ is
(A) -18.
(B) 12.
(C) 15.
(D) 27.
(E) 45.
(16th American High School Mathematics Examination, 1965)
[Solution] Let $f(x)=(x+a) g(x)$, then we have
$$
\begin{aligned}
& x^{4}+4 x^{3}+6 p x^{2}+4 q x+r \\
= & x^{4}+(a+3) x^{3}+(3 a+9) x^{2}+(9 a+3) x+3 a,
\end{aligned}
$$

By comparing the coefficients on both sides, we get $a=1, p=2, q=3, r=3$.
Thus, $(p+q) r=15$.
Therefore, the answer is $(C)$.