F.4 maths

The equation x^2 - bx - 24 = 0 can be solved using the factor method.
That means -b = M + N, where M and N are the factors of -24.
Then (M,N) can be: (1,-24),(-1,24),(2,-12), ... ,(-4,6)
[(6,-4) is repeated. So as the following ones]
So b can be -23, 23, -10, ... , 2

x^2-bx-24=0

x(x-b)=24
x-b=24/x
-b=24/x-x
b=x-24/x

Assume x=2,
b=2-24/2
b=2-12
b=-10

Prove, x^2-bx-24=0.
=2^2-(-10)2-24
=4+20-24
=0

(x-8)(x+3)...so the answer is -5
(x+8)(x-3)... the answer is 5

b=5 or b=10

1.(x-8)(x+3)....so x^2-5x-24.......b=5
2.(x-12)(x+2)....so x^2-10x-24.....b=10