#### Answer

$-(x-4)(2x+9)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
-2x^2-x+36
,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
To factor the trinomial expression above, note that the value of $ac$ is $
-2(36)=-72
$ and the value of $b$ is $
-1
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,-72 \}, \{ 2,-36 \}, \{ 3,-24 \}, \{ 4,-18 \}, \{ 6,-12 \}, \{ 8,-9 \},
\\
\{ -1,72 \}, \{ -2,36 \}, \{ -3,24 \}, \{ -4,18 \}, \{ -6,12 \}, \{ -8,9 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
8,-9
\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-2x^2+8x-9x+36
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(-2x^2+8x)-(9x-36)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-2x(x-4)-9(x-4)
.\end{array}
Factoring the $GCF=
(x-4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x-4)(-2x-9)
\\\\=
(x-4)(-1)(2x+9)
\\\\=
-(x-4)(2x+9)
.\end{array}