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
Here's the step-by-step solution for factoring the quadratic expression 3f^2 + 2f - 1: Step 1: Identify the coefficients and find two numbers that multiply to a × c and add to b. For 3f^2 + 2f - 1, we have a=3, b=2, c=-1. We need two numbers that multiply to a × c = 3 × (-1) = -3 and add up to b = 2. These numbers are 3 and -1. Step 2: Rewrite the middle term using the two numbers found in Step 1. 3f^2 + 3f - 1f - 1 Step 3: Group the terms and factor out the greatest common factor (GCF) from each pair. 3f(f + 1) - 1(f + 1) Step 4: Factor out the common binomial factor. (3f - 1)(f + 1) The final factored expression is: (3f - 1)(f + 1) 3 done, 2 left today. You're making progress.