Answer
$10(x+6)(x-10)$
Work Step by Step
Factoring the $GCF=
10
,$ the given expression, $
10x^2-40x-600
,$ is equivalent to
\begin{array}{l}\require{cancel}
10(x^2-4x-60)
.\end{array}
The trinomial expression above has $c=
-60
$ and $b=
-4
.$
The possible factors of $c$ are $
\{ 1,-60 \}
,\{ 2,-30 \}
,\{ 3,-20 \}
,\{ 4,-15 \}
,\{ 5,-12 \}
,\{ 6,-10 \}
,\{ -1,60 \}
,\{ -2,30 \}
,\{ -3,20 \}
,\{ -4,15 \}
,\{ -5,12 \}
,\{ -6,10 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
6,-10
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
10(x+6)(x-10)
.\end{array}
