# How do you factor y=x^2 - 2x - 15 ?

May 28, 2018

$y = \left(x - 5\right) \left(x + 3\right)$

#### Explanation:

$\text{the factors of - 15 which sum to - 2 are - 5 and + 3}$

$y = \left(x - 5\right) \left(x + 3\right)$

May 28, 2018

$\left(x - 5\right) \left(x + 3\right)$

#### Explanation:

First, find two numbers that have a sum of -2 (the second term) and have a product of -15 (the third term)
Multiples of 15:
1 | 15
3 | 5
$- 5 \cdot 3 = - 15$ and $- 5 + 3 = - 2$
Use this to "split the middle" of the polynomial
${x}^{2} - 5 x + 3 x - 15$
Factor
$x \left(x - 5\right) + 3 \left(x - 5\right)$
$\left(x - 5\right) \left(x + 3\right)$