Question

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

Answer 1

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.