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: 2

$(2x+1)(x+4)$

In accordance with the rules of factoring trinomials, we need two integers whose product is $8$ and whose sum is $9$. These numbers are $1$ and $8$. Therefore, we can express the middle term $9x$ as $1x+8x$ and proceed to factoring by grouping: $2x^{2}+9x+4$ =$2x^{2}+1x+8x+4$ =$x(2x+1)+4(2x+1)$ =$(2x+1)(x+4)$