# Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5 - Page 399: 10

(x+3)(x+5)

#### Work Step by Step

$x^{2}$ + 8x + 15 step 1. Enter x as the first term of each factor $x^{2}$ + 8x + 15 = (x+)(x+ _) Step 2. To find the second term of each factor, we must find two integers whose product is 15 and whose sum is 8 List pairs of factors of the constant, 15 (1,15)(3,5) step 3. The correct factorization of $x^{2}$ + 8x + 15 is the one in which the sum of the Outside and Inside products is equal to 8x. So (3,5) satisfy the condition $x^{2}$ + 8x + 15 = $x^{2}$ +3x+5x + 15 = (x+3)(x+5)

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