Factorize the trinomial x2 + x - 12. Find the values of b and c, and the two integers r and s.

Here's the solution to the factorization problem:

3.2.1 What is the value of $b$ and $c$ in the trinomial?
The general form of a trinomial is $ax^2 + bx + c$.
Comparing $x^2 + x - 12$ with $ax^2 + bx + c$:
$b = \boxed{1}$
$c = \boxed{-12}$

3.2.2 Use the table below to determine the two integers, $r$ and $s$.
We need two integers whose product is $c = -12$ and whose sum is $b = 1$.

Factors of -12	Product of the two factors	Sum of the two factors	Result
1, -12	-12	-11	No
-1, 12	-12	11	No
2, -6	-12	-4	No
-2, 6	-12	4	No
3, -4	-12	-1	No
-3, 4	-12	1	Yes

The two integers are $\boxed{-3 \text{ and } 4}$.

3.2.3 In the table below, the written explanation of the steps have been provided, show the mathematical steps for the explanations given.
Factorize $x^2 + x - 12$

Mathematical steps	Explanation
$x^2 + 4x - 3x - 12$	Rewrite the middle term of the trinomial using the values from the chart above.
$(x^2 + 4x) + (-3x - 12)$	Group pairs of terms.
$x(x + 4)$	Factor out the HCF of the first group.
$-3(x + 4)$	Factor out the HCF of the second group.
$(x + 4)(x - 3)$	Factor out HCF of the two terms.
$(x + 4)(x - 3)$	The final factorized answer.