To add the polynomials \( x^2 - 12 \) and \( 3x^2 + 15 \), you combine like terms, which are terms with the same variable raised to the same power.

Here's how you do it:

1. **Identify like terms**:
   - \( x^2 \) terms: \( x^2 \) and \( 3x^2 \)
   - Constant terms: \( -12 \) and \( 15 \)

2. **Add the like terms**:
   - For the \( x^2 \) terms: \( x^2 + 3x^2 = 4x^2 \)
   - For the constants: \( -12 + 15 = 3 \)

3. **Combine the results**:
   - The resulting polynomial is \( 4x^2 + 3 \).

So, the sum of the polynomials \( x^2 - 12 \) and \( 3x^2 + 15 \) is \( 4x^2 + 3 \).

Would you like more details or have any questions about this? Here are some related questions you might find helpful:

1. How do you subtract polynomials?
2. What is the difference between adding and multiplying polynomials?
3. How do you multiply polynomials?
4. What is the standard form of a polynomial?
5. How do you factor polynomials?
6. How do you divide polynomials?
7. Can you add polynomials with different degrees?
8. What are the applications of polynomials in real life?

**Tip**: When adding or subtracting polynomials, always align like terms (terms with the same degree) to ensure accuracy.

Learn how to add polynomials x^2 - 12 and 3x^2 + 15 with a step-by-step solution. This problem covers key algebraic concepts, including polynomials and combining like terms. Suitable for students in Grades 7-9.

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