solve x^2+5x+6 by factoring

Start by finding two numbers whose product is 6.

These are:

1 and 6

2 and 3

Now see if either pair adds to 5. 

Clearly, 2 and 3 do.  

So x^2 + 5x + 6 can be factored as (x + 2)(x + 3)

.