In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. find algebraically all possible
values of b.

To factor (x² +10x+24); you first have to ask yourself, what 2 numbers will multiply and give me positive 24, but add and give me positive 10? After listing your factors, (1,24)(2,12)(3,8)and (4,6); you decide that (4*6)=24 & adds to get you 10. Meaning that (x²+10x+24) factors are (x+4)(x+6). 
Now algebraically, there wouldn't be any other possible value of b, 6, because if you put (-6) & (4), those numbers will multiply and give you (-24) and add & give you (-2); & that is not what you're looking for. 

I hope I explained this enough for you to understand. (:

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