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You've uploaded a math exercise (Exercise 6.4) that focuses on various algebraic division problems. It contains different types of division tasks such as dividing polynomials, simplifying fractions involving variables, and using the long division method to solve equations.

### Here’s a breakdown of the types of questions:

1. **Division of Algebraic Expressions:**
   - These problems involve simplifying and dividing algebraic terms, as seen in questions like \( \frac{-49ab^3c^5}{-7ab^2c^3} \).

2. **Polynomial Division:**
   - Questions like \( \frac{16xy - 8x^3y + 12x^2y^3}{-4xy^2} \) involve simplifying polynomials.

3. **Long Division with Polynomials:**
   - Problems like \( 10 + 12y - 4y^2 \div (y+1) \) involve using the polynomial long division method.

4. **Quotient and Remainder:**
   - These tasks, such as \( (2x^3 + 4x + 8x^2 + 6) \div (2x^2 + 4 + x) \), require determining both the quotient and the remainder when dividing polynomials.

Would you like me to walk through the solution for a specific problem from this sheet? Feel free to point to any question, and I can assist in solving it.

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Here are 5 related questions to expand on these concepts:

1. How do you simplify the division of two algebraic expressions with multiple variables?
2. What are the steps for performing long division on polynomials?
3. How do you identify the quotient and remainder in polynomial division?
4. What techniques are helpful when simplifying complex polynomial expressions?
5. Can you apply synthetic division to higher-degree polynomials, and how?

**Tip:** Always ensure that the polynomials are arranged in descending order of powers before starting polynomial long division.

Division of algebraic expressions, polynomial division, and finding quotients and remainders (Exercise 6.4).

This page provides detailed solutions to algebraic division problems and polynomial long division, including finding the quotient and remainder from Exercise 6.4. Key concepts such as algebraic expressions, polynomial simplification, and long division are covered, suitable for Grades 9-11.

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