#### Answer

(x+3)(2x+1)

#### Work Step by Step

$2x^{2}$ + 7x +3
step 1. Find two first terms whose product is $2x^{2}$
$2x^{2}$ +7x +3 =(2x__)(x__)
Step 2. To find the second term of each factor, we must find two integers whose product is 3 and whose sum is 7
List pairs of factors of the constant, 3
(1,3)
step 3. The correct factorization of $2x^{2}$ +7x +3 is the one in which the sum of the Outside and Inside products is equal to 7x
list of the possible factorization :
(x+3)(2x+1)= $2x^{2}$ +7x +3
So, (x+3)(2x+1) is the solution.