# Is it possible to factor y=x^2 +8x+15? If so, what are the factors?

Dec 24, 2015

$y = {x}^{2} + 8 x + 15 = \textcolor{g r e e n}{\left(x + 3\right) \left(x + 5\right)}$

#### Explanation:

Since $\left(x + a\right) \left(x + b\right) = {x}^{2} + \left(a + b\right) x + a b$

we need to find two numbers $a$ and $b$
such that
$\textcolor{w h i t e}{\text{XXX}} a + b = 8$
and
$\textcolor{w h i t e}{\text{XXX}} a b = 15$

Checking factors of $15$ we quickly come up with $3$ and $5$ which sum to $8$