we are given
![x^2 +3x -10](https://img.qammunity.org/2019/formulas/mathematics/middle-school/yrkp6vvkz41tk3bk9hvoyfvuim5kvymiic.png)
it's factor as (x+p)(x+q)
so, we can write as
![x^2 +3x -10= (x+p)(x+q)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/8d7xwb9dzuncgugwdlv4j0r1fmx515bta9.png)
we can simplify it
![x^2 +3x -10= x^2 +(p+q)x +pq](https://img.qammunity.org/2019/formulas/mathematics/middle-school/j5pnvg48tbpbsy62lunp3t53860mgk87wx.png)
now, we can compare both sides
coefficient of x must be equal
so, we get
![3= (p+q)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/qpuubiy9i40moz23lndxxcixgbtqumw7rw.png)
![(p+q)=3](https://img.qammunity.org/2019/formulas/mathematics/middle-school/pbnla0462mtuzlxyddk42dgbd4nl18o2oq.png)
now, we can look at the table where p+q =3
so, we can see that when p+q=3 .... then p=-2 and q=5
so, option-A.......Answer