## Thinking Mathematically (6th Edition)

$5x^{2}$ - 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