What are the values of b and c in the trinomial x2 + 5x + 6, and what are the two integers r and s?

here are the solutions to Activity 3:

3.1.1 What is the value of $b$ and $c$ in the trinomial?
Comparing $x^2 + 5x + 6$ to the general form $x^2 + bx + c$:
$b = \boxed{5}$
$c = \boxed{6}$

3.1.2 Use the table below to determine the two integers, $r$ and $s$.

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 $\neq 5$
$-1$ and $-6$	$(-1) \times (-6) = 6$	$(-1) + (-6) = -7$	$\boxed{\text{product } = 6 \text{ but sum } \neq 5}$
2 and 3	$\boxed{2 \times 3 = 6}$	$\boxed{2 + 3 = 5}$	$\boxed{\text{product } = 6 \text{ and sum } = 5}$
$-2$ and $-3$	$(-2) \times (-3) = 6$	$(-2) + (-3) = -5$	$\boxed{\text{product } = 6 \text{ but sum } \neq 5}$

Which two integers will correctly provide the values of $b$ and $c$ in the expression $x^2 + 5x + 6$?
The two integers are $\boxed{2 \text{ and } 3}$.

3.1.3 Rewrite $x^2 + 5x + 6$ as an equivalent expression in the form $x^2 + rx + sx + 6$.
Using $r=2$ and $s=3$:

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

The equivalent expression is $\boxed{x^2 + 2x + 3x + 6}$.

3.1.4 Use the knowledge obtained from activity 2 on grouping and the distributive property to factorize the expression.