#### Answer

(x-1)(2x-3)

#### Work Step by Step

$2x^{2}$ - 5x + 3= (x-1) (____)
step 1. Find two first terms whose product is $2x^{2}$
$2x^{2}$ - 5x +3 = (x-1) (2x__)
Step 2. To find the second term of each factor, we must find two integers whose product is 3 and whose sum is -5
List pairs of factors of the constant, 3
(1,3)(-1,-3)
step 3. The correct factorization of $2x^{2}$ -5 x +3 is the one in which the sum of the Outside and Inside products is equal to -5x.
list of the possible factorization :
(x+1)(2x+3) = $2x^{2}$+5x+3
(x-1)(2x-3) = $2x^{2}$ - 5x +3
So, (x-1)(2x-3) is the solution