To determine the two integers, r and s, for the trinomial x² + x - 12, we need to find two numbers that multiply to the constant term (-12) and add up to the coefficient of the middle term ($

3.2.2

To determine the two integers, $r$ and $s$, for the trinomial $x^2 + x - 12$, we need to find two numbers that multiply to the constant term ($-12$) and add up to the coefficient of the middle term (1).

| Factors of $-12$ | Product of the two factors | Sum of the two factors | Result | | :--------------- | :------------------------- | :--------------------- | :----- | | $1, -12$ | $-12$ | $-11$ | | | $-1, 12$ | $-12$ | 11 | | | $2, -6$ | $-12$ | $-4$ | | | $-2, 6$ | $-12$ | 4 | | | $3, -4$ | $-12$ | $-1$ | | | $\mathbf{-3, 4}$ | $\mathbf{-12}$ | $\mathbf{1}$ | Correct |

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

3.2.3

To factorize $x^2 + x - 12$:

| Step | Mathematical steps | Explanation | | :--- | :-------------------------------- | 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