Question 104687
We want to find the values for a and b that make this true. 
{{{x^2 - 5sx -24s^2=(x+a)(x+b)}}}
If we expand the equation in terms of a and b, we can find what relationships need to be met to solve the problem. 
Note, the terms a and b will also include an s term for each. 
Don't let that throw you off, it acts like a constant.
{{{(x+a)(x+b)=x^2+(a+b)x+ab}}}
Let's compare terms in the original equation:
1.{{{ (a+b)x=-5sx}}} or
{{{a+b =-5s}}}
2.{{{ab=-24s^2}}}
Let's use equation 2 and look for factors of {{{-24s^2}}} that when summed equal -5s (Equation 1).
Integer factors of {{{24s^2}}} are (1s,24s),(2s,12s),(3s,8s),(4s,6s). 
(3s,8s) looks promising since their difference is 5s. 
Now we need to get the signs right. 
{{{-8s+3s=-5s}}} and {{{(-8s)(3s)=-24s^2}}} 
{{{x^2 - 5sx -24s^2=(x-8s)(x+3s)}}}