# How do you factor the expression x^2+8x+15?

Jan 2, 2016

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

#### Explanation:

Find $2$ integers whose sum is $8$ and whose product is $15$.

These numbers are $3$ and $5$, since

$3 + 5 = 8$
$3 \times 5 = 15$

Use the numbers $3$ and $5$ in two binomials, as follows:

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

This is ${x}^{2} + 8 x + 15$ in factored form.

You can check your work by redistributing and seeing if you get ${x}^{2} + 8 x + 15$.

$\left(x + 3\right) \left(x + 5\right) = x \left(x\right) + 5 x + 3 x + 3 \left(5\right) = {x}^{2} + 8 x + 15$