13. \( \left(x^{2}-4 x-21\right) \div(x+3) \)

To perform the division \(\left(x^{2} - 4x - 21\right) \div (x + 3)\), you can use polynomial long division or factoring. Here's a straightforward method using factoring: 1. **Factor the numerator:** The quadratic expression \(x^{2} - 4x - 21\) can be factored by finding two numbers that multiply to \(-21\) and add to \(-4\). These numbers are \(-7\) and \(3\). \[ x^{2} - 4x - 21 = (x - 7)(x + 3) \] 2. **Set up the division:** \[ \frac{(x - 7)(x + 3)}{x + 3} \] 3. **Simplify:** You can cancel the \((x + 3)\) terms in the numerator and the denominator (provided \(x \neq -3\) to avoid division by zero): \[ \frac{(x - 7)\cancel{(x + 3)}}{\cancel{x + 3}} = x - 7 \] So, the result of the division is: \[ x - 7 \]