To divide the expression \( \frac{x^2 - 7}{x + 3} \), we can perform polynomial division.

### Steps for Polynomial Division:
1. **Divide the first term of the numerator by the first term of the denominator**: 
   - Divide \(x^2\) by \(x\), which gives \(x\).

2. **Multiply the entire divisor by this result**: 
   - Multiply \(x + 3\) by \(x\), which gives \(x^2 + 3x\).

3. **Subtract this result from the original numerator**:
   - Subtract \((x^2 + 3x)\) from \(x^2 - 7\), giving \( -3x - 7 \).

4. **Repeat the division process** with the new expression \(-3x - 7\).

5. **Divide the first term of the new numerator by the first term of the denominator**: 
   - Divide \(-3x\) by \(x\), which gives \(-3\).

6. **Multiply the entire divisor by this result**: 
   - Multiply \(x + 3\) by \(-3\), which gives \(-3x - 9\).

7. **Subtract this result from the new numerator**:
   - Subtract \((-3x - 9)\) from \(-3x - 7\), giving a remainder of \(2\).

### Final Result:
The quotient is \(x - 3\), and the remainder is \(2\). Therefore, the division of \( \frac{x^2 - 7}{x + 3} \) results in:

\[
\frac{x^2 - 7}{x + 3} = x - 3 + \frac{2}{x + 3}
\]

Would you like any additional details or have any questions about this process?

### Related Questions:
1. How would you divide \(x^3 - 9x + 5\) by \(x - 2\)?
2. What happens if you perform polynomial division and the remainder is zero?
3. How can synthetic division be used for the same problem?
4. What is the long division method for dividing polynomials, and how does it differ from synthetic division?
5. How do you factor the polynomial \(x^2 - 7\) completely?

### Tip:
When performing polynomial division, always align like terms to avoid mistakes during subtraction.

Learn how to divide the polynomial x^2 - 7 by x + 3 using step-by-step polynomial division. Understand the process and get the quotient x - 3 with a remainder of 2. Suitable for high school students studying advanced algebra.

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