Factor: \( 8 v^{2}+6 v-5 \)

To factor the quadratic expression \( 8v^{2} + 6v - 5 \), we can start by looking for two numbers that multiply to the product of the leading coefficient and the constant term (which is \( 8 \times -5 = -40 \)) and add up to the middle coefficient (which is \( 6 \)). The numbers that fit this description are \( 10 \) and \( -4 \). Now, we rewrite the middle term using these numbers: \( 8v^{2} + 10v - 4v - 5 \). Next, we group the terms: \( (8v^{2} + 10v) + (-4v - 5) \). Factoring out the common factors in each group gives us: \( 2v(4v + 5) - 1(4v + 5) \). Now, we can factor out the binomial: \( (2v - 1)(4v + 5) \). Thus, the factored form of the expression \( 8v^{2} + 6v - 5 \) is \( (2v - 1)(4v + 5) \).