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 the greatest common factor (GCF) of all terms in the expression 2x^2 - 8x - 12. The terms are 2x^2, -8x, and -12. The numerical coefficients are 2, -8, and -12. The greatest common factor of these numbers is 2. There is no common variable factor since the last term, -12, does not contain x. Step 2: Factor out the GCF from each term. 2x^2 - 8x - 12 = 2(x^2) - 2(4x) - 2(6) 2(x^2 - 4x - 6) Step 3: Check if the quadratic expression inside the parenthesis, x^2 - 4x - 6, can be factored further. We look for two numbers that multiply to -6 and add to -4. The pairs of integer factors for -6 are (1, -6), (-1, 6), (2, -3), and (-2, 3). Their sums are: 1 + (-6) = -5 -1 + 6 = 5 2 + (-3) = -1 -2 + 3 = 1 None of these sums equal -4. Therefore, x^2 - 4x - 6 cannot be factored further over integers. The factorised expression is: 2(x^2 - 4x - 6) 3 done, 2 left today. You're making progress.