2. If $2 x^{2}+7 x y-15 y^{2}+a x+b y+3$ can be factored into the product of two linear polynomials with integer coefficients, where $a$ and $b$ are real numbers, then the minimum value of $a+b$ is $\qquad$
$$
\begin{array}{c}
\text { If the original expression is }=(x+5 y)(2 x-3 y)+a x+b y+3, \\
\text { then }(a, b)=(-5,-12),(5,12),(-7,4),(7,-4). \\
\text { Therefore, }(a+b)_{\text {min }}=-17.
\end{array}
$$