factor. x^2-x-6=? and x^2-5x-24=?.... i don't understand how u could factor these??

x^2 - x - 6

list factors of -6,
-6 x 1 = -6
6 x -1 = -6
-3 x 2 = -6
3 x -2 = -6

which factors of -6, when added, = -1
-6 + 1 = -5 N0
6 + -1 = 5 NO
-3 + 2 = -1 YES

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

x^2 - 5x - 24
list factors of -24,
-24 x 1 = -24
24 x -1 = -24
-12 x 2 = -24
12 x -2 = -24
-6 x 4 = -24
6 x -4 = -24
-8 x 3 = -24
8 x -3 = -24

which factors of 24, when added, = -5
24 + -1 = 23 N0
-24 + 1 = -23 NO
-12 + 2 = -10 NO
12 + -2 = 10 NO
-6 + 4 = -2 NO
6 + -4 = 2 NO
-8 + 3 = -5 YES

x^2 - 5x - 24 = (x - 8)(x + 3)