Factor the following:

1) x2 + 7x + 6

   Following the explicit rules, a = 1, b = 7, c = 6 in this case. 
   ac = (1)(6) = 6. 
   So we need to find the two factors of 6 that add up to 7.
   Factors of 6 are: 1 and 6, -1 and -6, 2 and 3, -2 and -3
   Factors of 6 that add up to 7 are +1 and +6.
   Thus, split 7x into x + 6x.

   x2 + 7x + 6 = x2 + x + 6x + 6
               = x(x + 1) + 6(x + 1)
               = (x + 1)(x + 6)

2) 4x2 + 5x - 6
   a = 4, b = 5, c = -6
   ac = (4)(-6) = -24
   Factors of -24 that add up to 5 are +8 and -3
   Thus, 5x = 8x - 3x
   
   4x2 + 5x - 6 = 4x2 + 8x - 3x - 6
                = 4x(x + 2) - 3(x + 2)
                = (x + 2)(4x - 3)