Remember that the product of two binomials on a single variable is a trinomial of the form:
![(w+a)(w+b)=w^2+(a+b)w+ab](https://img.qammunity.org/2023/formulas/mathematics/college/gkb03u8tiujwbmxw609qkikgehnk0msv1j.png)
Comparing with the coefficients of the trinomial:
![w^2+12w-13](https://img.qammunity.org/2023/formulas/mathematics/college/v6yb8cljm2yqurqepdrtdzsthugw52rw6k.png)
We should find two numbers a and b such that a+b=12 and a*b=-13.
Since the product a*b is negative, one number should be negative and the other should be positive. Notice that 13+(-1)=12 and (13)(-1)=-13. Then those numbers are 13 and -1. Therefore:
![w^2+12w-13=(w+13)(w-1)](https://img.qammunity.org/2023/formulas/mathematics/college/l1v0feh8ddnm2hwzxv48623ybxrkri52jq.png)