Identify b and c for x2 + 5x + 6.

Factors of 6	Product of the two factors	Sum of the two factors	Result
1 and 6	$1 \times 6 = 6$	$1 + 6 = 7$	product = 6 but sum $\neq$ 5
2 and 3	$2 \times 3 = 6$	$2 + 3 = 5$	product = 6 and sum = 5
-2 and -3	$(-2) \times (-3) = 6$	$(-2) + (-3) = -5$	product = 6 but sum $\neq$ 5

The two integers that correctly provide the values of $b$ and $c$ are $\boxed{2 \text{ and } 3}$.

Using $r=2$ and $s=3$:

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

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

Group the terms:

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

Factor out common factors from each group:

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

Factor out the common binomial $(x + 2)$:

$$\boxed{(x + 2)(x + 3)}$$