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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Here are the solutions for the factorization of x^2 + x - 12. 3.2.1 What is the value of b and c in the trinomial? The standard form of a trinomial is ax^2 + bx + c. Comparing x^2 + x - 12 with ax^2 + bx + c: b = 1 c = -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 | 1 × (-12) = -12 | 1 + (-12) = -11 | | | -1, 12 | -1 × 12 = -12 | -1 + 12 = 11 | | | 2, -6 | 2 × (-6) = -12 | 2 + (-6) = -4 | | | -2, 6 | -2 × 6 = -12 | -2 + 6 = 4 | | | 3, -4 | 3 × (-4) = -12 | 3 + (-4) = -1 | | | -3, 4 | -3 × 4 = -12 | -3 + 4 = 1 | Correct | The two integers are -3 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. | 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. | The final factorized answer is (x+4)(x-3). Send me the next one 📸