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
Step 1: Determine the values of b and c for x^2 + x - 12. The general form of a trinomial is ax^2 + bx + c. Comparing x^2 + x - 12 to ax^2 + bx + c: a = 1 b = 1 c = -12 a) The value of b is 1. b) The value of c is -12. Step 2: Complete the table for finding integers r and s for x^2 + x - 12. We need two integers r and s such that their product r × s = c = -12 and their sum r + s = 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 | Not 1 | | -1 and 12 | -1 × 12 = -12 | -1 + 12 = 11 | Not 1 | | 2 and -6 | 2 × (-6) = -12 | 2 + (-6) = -4 | Not 1 | | -2 and 6 | -2 × 6 = -12 | -2 + 6 = 4 | Not 1 | | 3 and -4 | 3 × (-4) = -12 | 3 + (-4) = -1 | Not 1 | | -3 and 4 | -3 × 4 = -12 | -3 + 4 = 1 | Is 1 | The two integers are -3 and 4. Step 3: Show the mathematical steps for factoring x^2 + x - 12. | Explanation | Mathematical steps