Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3 - Page 255: 12

$(n+5)(n-9)$

The following pairs of numbers give a product of $ -45 :$ \begin{array}{l}\require{cancel} \{ 1,-45 \} \text{ } \{ -1,45 \} \text{ } \{ 3,-15 \} \text{ } \{ -3,15 \} \text{ } \{ 5,-9 \} \text{ } \{ -5,9 \} .\end{array} Of these pairs, the one which gives a sum of $ -4 $ is the pair $\{ 5,-9 \}.$ Hence, the factored form of the given expression, $ n^2-4n-45 $ is \begin{array}{l}\require{cancel} (n+5)(n-9) .\end{array}