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 5a^2+2a-5 is a quadratic trinomial. To "solve" an expression typically means to simplify it or factor it. 1. Simplification: The terms 5a^2, 2a, and -5 are not like terms (they have different powers of a or are constants), so they cannot be combined further. The expression is already in its simplest form. 2. Factoring: To factor a quadratic expression of the form Ax^2+Bx+C, we look for two numbers that multiply to AC and add to B. For 5a^2+2a-5: A=5, B=2, C=-5. AC = (5)(-5) = -25. We need two numbers that multiply to -25 and add to 2. The pairs of integer factors for -25 are: • (1, -25) sum is -24 • (-1, 25) sum is 24 • (5, -5) sum is 0 None of these pairs sum to 2. Therefore, the expression cannot be factored over integers. Since the expression cannot be simplified or factored further over integers, it is already in its most basic form. The expression is already in its simplest form: 5a^2+2a-5