Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5: 22

(x+2)(3x+1)

Work Step by Step

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

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