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: Identify b and c in the trinomial x^2 + x - 12. The general form of a quadratic trinomial is ax^2 + bx + c. Comparing x^2 + x - 12 with ax^2 + bx + c: a = 1 b = 1 c = -12 b = 1 c = -12 Step 2: Determine the two integers, r and s, whose product is -12 and sum is 1. We need two numbers that multiply to c = -12 and add up to b = 1. Let's list factors of -12: • 1 × (-12) = -12, Sum: 1 + (-12) = -11 • -1 × 12 = -12, Sum: -1 + 12 = 11 • 2 × (-6) = -12, Sum: 2 + (-6) = -4 • -2 × 6 = -12, Sum: -2 + 6 = 4 • 3 × (-4) = -12, Sum: 3 + (-4) = -1 • -3 × 4 = -12, Sum: -3 + 4 = 1 The two integers are -3 and 4. | Factors of -12 | Product of the two factors | Sum of the two factors | Result | | :------------- | :------------------------- | :--------------------- | :----- | | 1, -12 | -12 | -11 | | | -1, 12 | -12 | 11 | | | 2, -6 | -12 | -4 | | | -2, 6 | -12 | 4 | | | 3, -4 | -12 | -1 | | | -3, 4 | -12 | 1 | ✓ | Step 3: Complete the table for factorizing x^2 + x - 12. Using the integers 4 and -3 from Step 2, we rewrite the middle term x as 4x - 3x. | 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. | Send me the next one 📸