Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Concept and Vocabulary Check - Page 399: 9



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.
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