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