# How do you factor x^2+14x+45?

Mar 31, 2017

$\left(x + 5\right) \left(x + 9\right)$

#### Explanation:

In order to the trinomial ${x}^{2} + 14 x + 45$

Begin by finding the factors for the first term

${x}^{2} = x \cdot x$

Place those factors as the first term in each parenthesis

$\left({x}_{_}\right) \left({x}_{_}\right)$

Since both signs of the trinomial are positive you will be adding the factors and both signs will be positive.

$\left(x {+}_{_}\right) \left(x {+}_{_}\right)$

Now determine the factors of the third term

$45 = 1 \cdot 45 , 3 \cdot 15 , 5 \cdot 9$

We need the factors that will add up to the middle term
$14 = 5 + 9$

Place these factors as the second term in each of the parenthesis.

$\left(x + 5\right) \left(x + 9\right)$

Mar 31, 2017

$\left(x + 5\right) \left(x + 9\right)$

#### Explanation:

The two numbers that add up to $14$, and multiply to $45$ and $9$ and $5$.

$\left(x + 5\right) \left(x + 9\right)$

Mar 31, 2017

$\left(x + 5\right) \left(x + 9\right)$

#### Explanation:

The two numbers that add up to $14$, and multiply to $45$ and $9$ and $5$.

$\left(x + 5\right) \left(x + 9\right)$