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The image you have uploaded contains a Learning Activity Sheet (LAS) for Mathematics 10, with a focus on dividing polynomials by binomials using the long division method.

### Key Concepts from the Sheet:

1. **Long Division of Polynomials:**
   - This is used when dividing a polynomial by a binomial, especially when the numerator and denominator do not have common factors.
   - Write the dividend (the polynomial to be divided) and the divisor (the binomial) in standard form, with terms arranged from highest to lowest degree.

2. **Example:**
   The division process for the example \((3x^2 - 11x + 9) \div (x + 3)\) is broken down step by step:
   - Divide the first term of the dividend by the first term of the divisor.
   - Multiply the divisor by this result and subtract from the dividend.
   - Repeat the steps with the remainder until the degree of the remainder is less than the degree of the divisor.

   For this specific example, the result of the division is:
   \[
   3x^2 - 11x + 9 \div (x + 3) = 3x - 2 + \frac{-15}{x + 3}
   \]

3. **Steps in Polynomial Long Division:**
   - Write the dividend and the divisor.
   - Divide the first term of the dividend by the first term of the divisor.
   - Multiply the divisor by this result and subtract it from the dividend.
   - Bring down the next term and repeat the process until there are no more terms to bring down.
   - If a remainder exists, express it as a fraction with the divisor as the denominator.

4. **Exercise:**
   The worksheet then provides exercises for the students to practice dividing polynomials using the synthetic division method.

Would you like me to work through one of the exercises or explain any part of the method in more detail?

Here are five related questions to deepen understanding:
1. How does synthetic division differ from the long division method in polynomial division?
2. What happens if the divisor is not a binomial in the form \( x + c \)?
3. Can you explain how the remainder theorem applies to polynomial division?
4. How can polynomial division be applied in solving real-world problems?
5. What role do degrees of polynomials play in the division process?

**Tip:** When dividing polynomials, always ensure both the dividend and divisor are in standard form—arrange terms from the highest to lowest power of \( x \).

How do you divide polynomials using the long division method?

Learn how to divide polynomials by binomials using the long division method. This step-by-step guide explains how to handle polynomial division problems, including solving (3x² - 11x + 9) ÷ (x + 3), and provides additional exercises.

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