Write the following expression in factored form. \( x^{2}-2 x-15 \) \( (x+1)(x-15) \) \( (x-1)(x+15) \) \( (x+3)(x-5) \) \( (x-3)(x+5) \)

To factor the quadratic expression \( x^{2} - 2x - 15 \), we need to find two numbers that: 1. **Multiply to** the constant term (**-15**). 2. **Add up to** the coefficient of the middle term (**-2**). Let's identify these numbers step by step: 1. **Find factors of -15:** - \( 1 \) and \( -15 \) → \( 1 \times (-15) = -15 \) and \( 1 + (-15) = -14 \) - \( -1 \) and \( 15 \) → \( -1 \times 15 = -15 \) and \( -1 + 15 = 14 \) - \( 3 \) and \( -5 \) → \( 3 \times (-5) = -15 \) and \( 3 + (-5) = -2 \) 2. **Select the pair that adds up to -2:** - The pair **\( 3 \) and \( -5 \)** satisfy both conditions. 3. **Write the factored form:** \[ x^{2} - 2x - 15 = (x + 3)(x - 5) \] **Among the given options:** - \( (x+1)(x-15) \) - \( (x-1)(x+15) \) - \( (x+3)(x-5) \) ✅ **Correct** - \( (x-3)(x+5) \) **Therefore, the correct factored form is:** \[ (x + 3)(x - 5) \]