Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 1

$(x+1)(x+6)$

The given expression, $ x^2+7x+6 ,$ has $c= 6 $ and $b= 7 .$ The possible factors of $c$ are $ \{ 1,6 \} ,\{ -1,-6 \} ,\{ 2,3 \} ,\{ -2,-3 \} $. The factors whose sum is equal to $b$ are $\{ 1,6 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (x+1)(x+6) .\end{array}