Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4 - Page 261: 1

$(3x+1)(x+2)$

In accordance with the rules of factoring trinomials, we need two integers whose product is 6 and whose sum is 7. These numbers are 1 and 6. Using this information, we factor the trinomial: $3x^{2}+7x+2$ =$3x^{2}+1x+6x+2$ =$x(3x+1)+2(3x+1)$ =$(3x+1)(x+2)$