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: 3

$(x+5)(x+8)$

The following pairs of numbers give a product of $ 40 :$ \begin{array}{l}\require{cancel} \{ 1,40 \} \text{ } \{ 2,20 \} \text{ } \{ 4,10 \} \text{ } \{ 5,8 \} .\end{array} Of these pairs, it is the pair $\{ 5,8 \}$ which gives a sum of $ 13 .$ Hence, the factored form of the given expression, $ x^2+13x+40 $ is \begin{array}{l}\require{cancel} (x+5)(x+8) .\end{array}