Factor \( 3 x^{2}+5 x-2 \)

To factor the quadratic expression \(3x^{2} + 5x - 2\), we can look for two numbers that multiply to \(3 \times -2 = -6\) and add up to \(5\). The numbers \(6\) and \(-1\) fit the bill. Now we can rewrite the middle term: \[ 3x^{2} + 6x - 1x - 2 \] Next, we group the terms: \[ (3x^{2} + 6x) + (-1x - 2) \] Factoring out the greatest common factors from each group gives us: \[ 3x(x + 2) - 1(x + 2) \] Now we can factor out the common binomial: \[ (3x - 1)(x + 2) \] Thus, the factored form of \(3x^{2} + 5x - 2\) is: \[ (3x - 1)(x + 2) \]