To factor x^2 + 5x + 6, we think of numbers that add up to +5 and whose product is 6. We can start by listing the factors of 6 and then getting their sums.
1 and 6-->7
-1 and -6--> -7
2 and 3--> 5
-2 and -3 --> -5
From the list, we see that 2 and 3 are the answers. So we form our binomial factors using +2 and +3 as second terms.
[tex]x^2+5x+6=(x+2)(x+3)[/tex]