# How do you factor the expression k^2 + 11k + 28?

Mar 16, 2018

$\left(k + 4\right) \left(k + 7\right)$

#### Explanation:

$\text{Consider the factors of 28 which sum to + 11}$

$\text{the factors of + 28 which sum to + 11 are + 7 and + 4}$

$\Rightarrow {k}^{2} + 11 k + 28 = \left(k + 4\right) \left(k + 7\right)$

Mar 16, 2018

$\left(k + 7\right) \left(k + 4\right)$

#### Explanation:

Start by looking at your first term: ${k}^{2}$

Now look at the signs of the second two terms: both are positive
From these observations, we know our factors will be:
(k+___)(k+_)

because k times k will get us ${k}^{2}$ , and both factors having a "+" sign means that our second and third terms will both be positive.

Now, what two numbers will equal 11 when added together, and 28 when multiplied together?
The two numbers are 7 and 4.

7+4=11
7*4=28

So these complete our factors, $k + 7$ and $k + 4$