#### Answer

$x^2+7x+12 = (x+3)~(x+4)$

#### Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$
Then we can factor the trinomial as follows:
$~x^2+bx+c = (x+r)~(x+s)$
Let's consider this trinomial: $~x^2+7x+12$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = 7$ and $r\times s = 12$. We can see that $3+4 = 7$ and $3\times 4 = 12$
We can factor the trinomial as follows:
$x^2+7x+12 = (x+3)~(x+4)$