Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.2 - Factoring Trinomials of the Form x2+bx+c - Exercise Set: 29

Answer

Chapter 6 - Section 6.2 - Exercise Set: 29 (Answer) $x^2 + 15x + 36$ = $(x + 3)(x + 12)$

Work Step by Step

Chapter 6 - Section 6.2 - Exercise Set: 29 (Solution) Factor : $x^2 + 15x + 36$ To begin by writing the first terms of the binomial factors $(x + \triangle)(x + \square)$ Next, to look for two numbers whose product is +36 and whose sum is +15. As the two numbers have a positive product and a positive sum, pairs of positive factors of 36 are to be investigated only. Factors of 36 $\Longleftrightarrow$ Sum of Factors 1,36 $\Longleftrightarrow$ 37 (Incorrect sum) 2,18 $\Longleftrightarrow$ 20 (Incorrect sum) 3,12 $\Longleftrightarrow$ 15 (Correct sum, so the two numbers are 3 and 12) 4,9 $\Longleftrightarrow$ 13 (Incorrect sum) 6,6 $\Longleftrightarrow$ 12 (Incorrect sum) Thus, $x^2 + 15x + 36$ = $(x + 3)(x + 12)$
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