已知 $(19 x-31)(13 x-17)-(17-13 x)(11 x-23)$ 可因式分解成 $(a x+b)(30 x+$ $c$ ), 其中 $a 、 b 、 c$ 均为整数, 求 $a+b+c$ 的值.
【答案】解：由题意得
$$
\begin{aligned}
& (19 x-31)(13 x-17)-(17-13 x)(11 x-23) \\
& =(19 x-31)(13 x-17)+(13 x-17)(11 x-23) \\
& =(13 x-17)(30 x-54)
\end{aligned}
$$

$$
\begin{aligned}
& =(a x+b)(30 x+c), \\
& \therefore a=13, b=-17, c=-54, \\
& \therefore a+b+c=-58 .
\end{aligned}
$$