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
To resolve the expression 2 ^2 + 13 + 15 into factors. Step 1: Let x = . Substitute x into the expression to form a quadratic equation. 2x^2 + 13x + 15 Step 2: Factor the quadratic expression by splitting the middle term. We need two numbers that multiply to 2 × 15 = 30 and add up to 13. These numbers are 3 and 10. 2x^2 + 3x + 10x + 15 Step 3: Group the terms and factor out common factors from each group. (2x^2 + 3x) + (10x + 15) x(2x + 3) + 5(2x + 3) Step 4: Factor out the common binomial factor (2x + 3). (2x + 3)(x + 5) Step 5: Substitute back for x. (2 + 3)( + 5) The factored expression is: (2 + 3)( + 5)