Factor by grouping. \[ 6 v^{2}-5 v-6 \]

To factor the quadratic expression \( 6v^{2} - 5v - 6 \) by grouping, follow these steps: 1. **Multiply the coefficient of \( v^2 \) by the constant term:** \( 6 \times (-6) = -36 \) 2. **Find two numbers that multiply to \(-36\) and add up to \(-5\):** The numbers are \(-9\) and \(4\), since: \[ -9 \times 4 = -36 \quad \text{and} \quad -9 + 4 = -5 \] 3. **Rewrite the middle term using these numbers:** \[ 6v^{2} - 9v + 4v - 6 \] 4. **Factor by grouping:** \[ (6v^{2} - 9v) + (4v - 6) = 3v(2v - 3) + 2(2v - 3) \] 5. **Factor out the common binomial factor \((2v - 3)\):** \[ (3v + 2)(2v - 3) \] **Final Factored Form:** \[ (3v + 2)(2v - 3) \]