Answer
(2x+3)(3x+4)
Work Step by Step
$6x^{2}$ +17x + 12= (2x+3) (____)
step 1. Find two first terms whose product is $6x^{2}$, so (2x,3x)(x,6x) are two options but it is given 2x in first factor so (2x,3x) is the correct option
$6x^{2}$ +17x + 12 = (2x+3) (3x___)
Step 2. To find the second term of each factor, we must find two integers whose product is 12 and whose sum is 17
List pairs of factors of the constant, 12
(1,12)(2,6)(3,4)
step 3. The correct factorization of $6x^{2}$ +17x + 12 is the one in which the sum of the Outside and Inside products is equal to 17x.
As it is given (2x+3) is the first factor
So, (2x+3)(3x+4) is the solution.
