Use the table below to determine the two integers, r and s. In the table below, the written explanation of the steps have been provided, show the mathematical steps for the explanations given.

3.2.2
To factor the trinomial $x^2 + x - 12$, we need to find two integers, $r$ and $s$, such that their product is $-12$ (the constant term) and their sum is 1 (the coefficient of the middle term, $x$).

Here is the completed table:

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

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

3.2.3
Here are the mathematical steps to factor $x^2 + x - 12$ using the values found in the table above:

Explanation	Mathematical steps
Rewrite the middle term of the trinomial using the values from the chart above.	$x^2 + 4x - 3x - 12$
Group the first two terms and the last two terms.	$(x^2 + 4x) + (-3x - 12)$
Factor out the greatest common factor from each group.	$x(x + 4) - 3(x + 4)$
Factor out the common binomial.	$\boxed{(x + 4)(x - 3)}$