In the equation x2 +10x + 24 = ( x + a) ( x + b), b is an integer. find algebraically all possible values of b.

Multiply
(x+a)(x+b) = x^2 + bx + ax + ab
looking at; x^2 + 10x + 24
can you see that

ab = 24
bx + ax = 10x
then
a + b = 10

use substitution: a = 10 - b

(10-b)b = 24
10b - b^2 = 24
-b^2 + 10b -24 = 0
now find the values for b using the quadratic equation. I'm on my phone so you'll have to plug the numbers in. let me know if you have any questions.

All you have to do is multiply