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
The expression shown is 2h^2 - 13x - 14. This contains two different variables, h and x. To apply the "splitting the middle term" method, the expression must be a quadratic in a single variable. Assuming the first term's variable was intended to be x, making the expression 2x^2 - 13x - 14, we proceed as follows: Step 1: Identify the coefficients and find two numbers that multiply to a × c and add to b. For 2x^2 - 13x - 14, we have a=2, b=-13, c=-14. We need two numbers that multiply to a × c = 2 × (-14) = -28 and add up to b = -13. Step 2: List integer pairs that multiply to -28 and check their sums. The integer pairs that multiply to -28 are (1, -28), (-1, 28), (2, -14), (-2, 14), (4, -7), and (-4, 7). Their respective sums are 1 + (-28) = -27, -1 + 28 = 27, 2 + (-14) = -12, -2 + 14 = 12, 4 + (-7) = -3, and -4 + 7 = 3. Step 3: Conclude based on the sums. Since none of these pairs sum to -13, the quadratic expression 2x^2 - 13x - 14 cannot be factored into linear factors with integer coefficients using the splitting the middle term method. Not factorable over integers What's next?