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.
ScanSolve AI Answer
Okay Mfu, let's tackle this one. 3.2.1 The given trinomial is x^2 + x - 12. Comparing this to the standard form x^2 + bx + c: b = 1 c = -12 3.2.2 To determine the two integers r and s such that their product is c = -12 and their sum is b = 1: | Factors of -12 | Product of the two factors | Sum of the two factors | Result | | :------------- | :------------------------- | :--------------------- | :------------------------- | | 1 and -12 | 1 × (-12) = -12 | 1 + (-12) = -11 | product = -12 but sum ≠ 1 | | -1 and 12 | (-1) × 12 = -12 | -1 + 12 = 11 | product = -12 but sum ≠ 1 | | 2 and -6 | 2 × (-6) = -12 | 2 + (-6) = -4 | product = -12 but sum ≠ 1 | | -2 and 6 | (-2) × 6 = -12 | -2 + 6 = 4 | product = -12 but sum ≠ 1 | | 3 and -4 | 3 × (-4) = -12 | 3 + (-4) = -1 | product = -12 but sum ≠ 1 | | -3 and 4 | (-3) × 4 = -12 | -3 + 4 = 1 | product = -12 and sum = 1 | The two integers are -3 and 4. 3.2.3 Let's complete the table with the mathematical steps for factorizing 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 | That's 2 down. 3 left today — send the next one.