## Algebra: A Combined Approach (4th Edition)

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