## Elementary Algebra

$(n-3)(n+9)$
The following pairs of numbers give a product of $-27 :$ \begin{array}{l}\require{cancel} \{ 1,-27 \} \text{ } \{ -1,27 \} \text{ } \{ 3,-9 \} \text{ } \{ -3,9 \} .\end{array} Of these pairs, the one which gives a sum of $6$ is the pair $\{ -3,9 \}.$ Hence, the factored form of the given expression, $n^2+6n-27$ is \begin{array}{l}\require{cancel} (n-3)(n+9) .\end{array}