1.54 If $2 x^{3}-h x+k$ has two factors $x+2$ and $x-1$, then the value of $2 h-3 k$ is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(E) 0.
(21st American High School Mathematics Examination, 1970)
[Solution] Let $f(x)=2 x^{3}-h x+k$. According to the problem, we have
$$
\begin{array}{l}
f(-2)=2 \cdot(-2)^{3}-h(-2)+k=2 h+k-16=0, \\
f(1)=2 \cdot 1^{3}-h \cdot 1+k=k-h+2=0 .
\end{array}
$$

From the above, we solve to get $h=6, k=4$, then $|2 h-3 k|=0$. Therefore, the answer is $(E)$.