This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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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 -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. | (x + 4)(x - 3) | Drop the next question! 📸