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Let's solve the problem by adding the two polynomial expressions:

**Polynomials to add:**
1. \( 5z - 2z^2 - 4z + 5 \)
2. \( 6z^2 + 3 - 7z \)

### Step 1: Combine like terms
- **Terms with \( z^2 \):**
  - From the first polynomial: \( -2z^2 \)
  - From the second polynomial: \( 6z^2 \)
  - Total: \( -2z^2 + 6z^2 = 4z^2 \)

- **Terms with \( z \):**
  - From the first polynomial: \( 5z - 4z = z \)
  - From the second polynomial: \( -7z \)
  - Total: \( z - 7z = -6z \)

- **Constant terms:**
  - From the first polynomial: \( 5 \)
  - From the second polynomial: \( 3 \)
  - Total: \( 5 + 3 = 8 \)

### Step 2: Write the final expression
The resulting polynomial after combining the terms is:
\[ 4z^2 - 6z + 8 \]

### Step 3: Match the result with the given options:
The correct option is:
- \( \boxed{4z^2 - 6z + 8} \)

Would you like any further details or clarifications?

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Here are 5 related questions you might find useful:
1. How do you subtract polynomials instead of adding them?
2. What happens when there are no like terms to combine?
3. How do you factor a quadratic polynomial like \( 4z^2 - 6z + 8 \)?
4. How do you multiply two polynomials?
5. What is the degree of the resulting polynomial?

**Tip**: Always line up like terms when adding or subtracting polynomials to avoid mistakes.

Add the polynomial expressions 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z.

Learn how to add the polynomials 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z. This step-by-step solution demonstrates how to combine like terms and simplify the expression. Suitable for students in Grades 8-10.

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