Factors of the trinomial ?

1)
x^2 + 2x - 24
= x^2 + 6x - 4x - 24
= (x^2 + 6x) - (4x + 24)
= x(x + 6) - 4(x + 6)
= (x + 6)(x - 4)

2)
x^2 + 5x + 6
= x^2 + 3x + 2x + 6
= (x^2 + 3x) + (2x + 6)
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)

-24 = 6 * (-4)
(x+6)(x-4)

6 = 2 * 3
(x+2)(x+3)