Answer
(x-2)(5x-3)
Work Step by Step
$5x^{2}$ - 13x + 6
step 1. Find two first terms whose product is $5x^{2}$
$5x^{2}$ -13x +6 =(5x__)(x__)
Step 2. To find the second term of each factor, we must find two integers whose product is 6 and whose sum is -13
List pairs of factors of the constant, 6
(1,6)(-1,-6)(2,3)(-2,-3)
step 3. The correct factorization of $5x^{2}$ -13x +6 is the one in which the sum of the Outside and Inside products is equal to -13x
list of the possible factorization :
(x-1)(5x-6)= $5x^{2}$ -11x +6
(x-2)(5x-3) = $5x^{2}$ -13x +6
So, (x-2)(5x-3) is the solution
Verification using FOIL
Two binomials can be quickly multiplied by using the FOIL method, in which F represents the product of the first terms in each binomial, O represents the product of the outside terms, I represents the product of the two inside terms, and L represents the product of the last,
(x-2)(5x-3)
F = x.5x = $5x^{2}$
O = x.-3 = -3x
I = -2.5x = -10x
L = -2.-3= 6
(x-2)(5x-3) = $5x^{2}$ -3x -10x +6
= $5x^{2}$ -13x +6
