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

To factor the quadratic expression \( 5x^{2}+2x-3 \), we can look for two numbers that multiply to \( 5 \times (-3) = -15 \) and add up to \( 2 \). Those numbers are \( 5 \) and \( -3 \). We rewrite the middle term using these numbers: \( 5x^{2} + 5x - 3x - 3 \). Now, we group the terms: \( (5x^{2} + 5x) + (-3x - 3) \). Factoring out common factors from each group gives us: \( 5x(x + 1) - 3(x + 1) \). Finally, we can factor out the common binomial: \( (5x - 3)(x + 1) \). So, the fully factored form is: \( (5x - 3)(x + 1) \).