Ans: A
$\begin{array}{rcl}
x^2+p(x+5)+q & \equiv & (x-2)(x+5)\\
x^2+px+(5p+q) & \equiv & x^2+3x-10
\end{array}$
$\begin{array}{rcl}
x^2+p(x+5)+q & \equiv & (x-2)(x+5)\\
x^2+px+(5p+q) & \equiv & x^2+3x-10
\end{array}$
By comparing the coefficients of both sides, we have
$\left\{ \begin{array}{ll}
p=3 & \ldots \unicode{x2460} \\
5p+q = -10 & \ldots \unicode{x2461}
\end{array} \right.$
Sub. $\unicode{x2460}$ into $\unicode{x2461}$, we have
$\begin{array}{rcl}
5(3) + q & = & -10 \\
q & = & -25
\end{array}$
