1. **Problem:** Divide $x^2 - 13x - 48$ by $x + 3$ using long division. 2. **Formula and rules:** For polynomial long division, divide the leading term of the dividend by the leading term of the divisor, multiply the divisor by this quotient, subtract from the dividend, and repeat with the remainder. 3. **Step 1:** Divide leading terms: $\frac{x^2}{x} = x$. 4. Multiply divisor by $x$: $(x + 3)(x) = x^2 + 3x$. 5. Subtract: $(x^2 - 13x - 48) - (x^2 + 3x) = -16x - 48$. 6. **Step 2:** Divide leading terms of remainder: $\frac{-16x}{x} = -16$. 7. Multiply divisor by $-16$: $(x + 3)(-16) = -16x - 48$. 8. Subtract: $(-16x - 48) - (-16x - 48) = 0$. 9. **Result:** Quotient is $x - 16$ with remainder $0$. **Final answer:** $$\boxed{x - 16}$$