#### Answer

$x^2+5x-24 = (x+8)~(x-3)$

#### 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: $~x^2+5x-24$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -24$. We can see that $(8)+(-3) = 5~$ and $(8)\times (-3) = -24$
We can factor the trinomial as follows:
$x^2+5x-24 = (x+8)~(x-3)$