# Chapter 6 - Section 6.2 - Factoring Trinomials of the Form x2+bx+c - Practice - Page 425: 3

Practice 3 (Answer) $x^{2} + 5x - 36$ $= (x + 9)(x - 4)$

#### Work Step by Step

Practice 3 (Solution) Factor : $x^{2} + 5x - 36$ Solution : $x^{2} + 5x - 36$ = ($x + \triangle$)($x + \square$) Now, to look for two numbers whose product is -36 and whose sum is +5. As the two numbers must have a negative product, pairs of factors with opposite signs of -36 are to be investigated. Factors of -36 $\Longleftrightarrow$ Sum of Factors 1,-36 $\Longleftrightarrow$ -35 36,-1 $\Longleftrightarrow$ 35 2,-18 $\Longleftrightarrow$ -16 18,-2 $\Longleftrightarrow$ 16 3,-12 $\Longleftrightarrow$ -9 12,-3 $\Longleftrightarrow$ 9 4,-9 $\Longleftrightarrow$ -5 9,-4 $\Longleftrightarrow$ 5 (Correct sum, so the numbers are 9 and -4) 6,-6 $\Longleftrightarrow$ 0 Thus, $x^{2} + 5x - 36 = (x + 9)(x - 4)$

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