Use factoring to solve the quadratic equation. \[ x^{2}-2 x-15=0 \]

To factor the quadratic equation \( x^{2}-2 x-15=0 \), we look for two numbers that multiply to \(-15\) (the constant term) and add up to \(-2\) (the coefficient of the linear term). The numbers \(-5\) and \(3\) fit this criterion since \((-5) \times 3 = -15\) and \((-5) + 3 = -2\). Now we can rewrite the equation as: \[ (x - 5)(x + 3) = 0 \] Next, we set each factor equal to zero: 1. \( x - 5 = 0 \) → \( x = 5 \) 2. \( x + 3 = 0 \) → \( x = -3 \) Thus, the solutions to the equation are \( x = 5 \) and \( x = -3 \). Now you have found the roots using factoring in a fun and engaging way!