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: List all pairs of integers whose product is -12. We are looking for two integers, r and s, such that their product r × s = -12 and their sum r + s = 1 (from the previous problem x^2 + x - 12, where c = -12 and b = 1). Step 2: Calculate the product and sum for each pair of factors. Fill in the table with the factors of -12, their products, and their sums. Mark the pair that results in a sum of 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 | ✓ | The two integers, r and s, are -3 and 4. 3 done, 2 left today. You're making progress.