You can put this solution on YOUR website! See my Lesson Plans on Factoring Trinomials from Basic Algebra, either in algebra.com or in my own website under "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then Chapter 2.
In this one you know it is going to be a product of two binomials (because they usually are!), and that it will start off with
(s _____)(s _____). The trick is to look at the LAST term which in this problem is 24. You have to find two numbers whose product is 24 such that you can add (or in certain cases subtract the numbers) and get -10. Sometimes you can think of the right combination of numbers immediately, and sometimes it takes longer. A systematic way to do this is to start with 1 in this way:
1*24
2*12
3*8
4*6
Since the next number that goes into 24 would be 6 (that is 6*4) it means that you have them all. Now in this case it is 4*6 that you need, so write this as
(s__4)(s__6) or (s__6)(s__4).
Next you have to make the middle term come out to a -10, so it will be -4*-6, and the final answer is
(s-4)(s-6)
