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, $x^2 + 15x + 36$ = $(x + 3)(x + 12)$
