Rewrite x2 + 5x + 6 in the form x2 + rx + sx + c.

From the previous steps, we identified that for the trinomial $x^2 + 5x + 6$, the two integers $r$ and $s$ whose product is 6 and sum is 5 are 2 and 3.
Therefore, we can rewrite the middle term $5x$ as $2x + 3x$.

$$x^2 + 2x + 3x + 6$$

We will group the terms and factor out the common factors.

$$x^2 + 2x + 3x + 6$$

Group the first two terms and the last two terms:

$$(x^2 + 2x) + (3x + 6)$$

Factor out the greatest common factor (HCF) from each group:

$$x(x + 2) + 3(x + 2)$$

Now, factor out the common binomial factor $(x + 2)$:

$$(x + 2)(x + 3)$$