Answer
$(x-5)(x-3)$
Work Step by Step
The 2 numbers whose product is $ac=
1(15)=15
$ and whose sum is $b=
-8
$ are $\left\{
-5,-3
\right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $
x^2-8x+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}