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To simplify the expression \((4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11)\), we need to combine like terms.

1. **Combine like terms:**
   - \(4x^3\): There are no other \(x^3\) terms, so it remains \(4x^3\).
   - \(-5x^2 + 2x^2\): This simplifies to \(-3x^2\).
   - \(6x\): There are no other \(x\) terms, so it remains \(6x\).
   - \(7 - 11\): This simplifies to \(-4\).

2. **Simplified expression:**
   \[
   4x^3 - 3x^2 + 6x - 4
   \]

The correct option is:

**C. \(4x^3 - 3x^2 + 6x - 4\)**

Would you like further details or explanations? Here are some related questions you might consider:

1. What is the general method to combine like terms in polynomial expressions?
2. How can we identify and group like terms in more complex polynomial expressions?
3. What are the rules for adding and subtracting polynomials?
4. Can polynomials be simplified further if given in factored form?
5. How can polynomial addition be represented graphically?

**Tip:** Always align and group similar terms vertically when adding or subtracting polynomials to avoid mistakes.

Simplify (4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11). Choose the correct answer from A, B, C, or D.

Learn how to simplify the polynomial expression (4x^3 - 5x^2 + 7) + (2x^2 + 6x - 11) by combining like terms. This exercise covers key algebraic concepts in polynomial simplification, making it suitable for students in Grades 9-12.

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