Question

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

values of b.

Answer 1

They want you to factor the left side so you get
`(x+4)(x+6)=(x+a)(x+b)` where b equals 4 or 6. That's probably the answer they're looking for, but it's not correct.
The right answer is found by foiling the right side so you get
`x^2+ax+bx+ab` and then solving for b, which gets you
`(10x-ax+24)/(x+a)`. That's the correct answer. There is an infinite number of possible values for b.