# Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5 - Page 399: 16

(x+9)(x-10)

#### Work Step by Step

$x^{2}$ - x -90 step 1. Enter x as the first term of each factor $x^{2}$ - x - 90= (x__)(x _) Step 2. To find the second term of each factor, we must find two integers whose product is -90 and whose sum is -1 List pairs of factors of the constant, -90 (1,-90)(-1,90)(-2,45)(2,-45)(3,-30)(-3,30)(5,-18)(-5,18)(6,-15)(-6,15)(9,-10)(-9,10) step 3. The correct factorization of $x^{2}$ - x - 90 is the one in which the sum of the Outside and Inside products is equal to -x. So (9,-10) satisfy the condition $x^{2}$ -x -90 = $x^{2}$ +9x -10x - 90= (x+9)(x-10)

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