Answer
$(x+5)(x-3)$
Work Step by Step
The 2 numbers whose product is $ac=
1(-15)=-15
$ and whose sum is $b=
2
$ are $\left\{
5,-3
\right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $
x^2-2x-15
,$ then the factored form is
\begin{array}{l}
x^2+5x-3x-15
\\\\=
(x^2+5x)-(3x+15)
\\\\=
x(x+5)-3(x+5)
\\\\=
(x+5)(x-3)
.\end{array}