# Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5: 11

(x+3)(x-5)

#### Work Step by Step

$x^{2}$ - 2x - 15 step 1. Enter x as the first term of each factor $x^{2}$ - 2x - 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 -2 List pairs of factors of the constant, -15 (1,-15)(-1,15)(3,-5)(-3,5) step 3. The correct factorization of $x^{2}$ - 2x - 15 is the one in which the sum of the Outside and Inside products is equal to -2x. So (3,-5) satisfy the condition $x^{2}$ -2x - 15 = $x^{2}$ +3x -5x - 15 = (x+3)(x-5)

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