Answer
$(x-6)(x-9)$
Work Step by Step
The two numbers whose product is $ac=
1(54)=54
$ and whose sum is $b=
-15
$ are $\{
-6,-9
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x^2-15x+54
$, is
\begin{array}{l}\require{cancel}
x^2-6x-9x+54
\\\\=
(x^2-6x)-(9x-54)
\\\\=
x(x-6)-9(x-6)
\\\\=
(x-6)(x-9)
.\end{array}
