Answer
$(n+4)(n-10)$
Work Step by Step
The following pairs of numbers give a product of $
-40
:$
\begin{array}{l}\require{cancel}
\{ 1,-40 \}
\text{ }
\{ -1,40 \}
\text{ }
\{ 2,-20 \}
\text{ }
\{ -2,20 \}
\text{ }
\{ 4,-10 \}
\text{ }
\{ -4,10 \}
\text{ }
\{ -5,8 \}
\text{ }
\{ 5,-8 \}
.\end{array}
Of these pairs, the one which gives a sum of $
-6
$ is the pair $\{
4,-10
\}.$
Hence, the factored form of the given expression, $
n^2-6n-40
$ is
\begin{array}{l}\require{cancel}
(n+4)(n-10)
.\end{array}
