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The image contains a math activity focused on polynomial division. The task asks to divide polynomials in a specific form, where \( \frac{P(x)}{D(x)} = \frac{Q(x)}{D(x)} + \frac{R(x)}{D(x)} \). An example is provided at the top of the page to illustrate how to perform the division:

\[
(x^4 + x^2 - 5) \div (x - 5) = x^3 + 5x^2 + 26x + 130 + \frac{645}{x - 5}
\]

Below this, five problems are presented for division:

1. \( (5x^2 - 17x - 15) \div (x - 4) \)
2. \( (6x^3 - 16x^2 + 17x - 6) \div (3x - 2) \)
3. \( (2x^4 + x^3 - 19x^2 + 18x + 5) \div (2x - 5) \)
4. \( (4x^5 + 6x^4 + 5x^2 - x - 10) \div (2x^2 + 3) \)
5. \( (4x^5 - 25x^4 + 40x^3 + 3x^2 - 18x) \div (x^2 - 6x + 9) \)

Lastly, the problem suggests the use of a technique called "synthetic division," which simplifies the procedure by working with just the coefficients.

Would you like me to solve one of these division problems step-by-step or explain the synthetic division method further? Feel free to ask for more details.

Here are 5 related questions you might find interesting:
1. How do you perform polynomial long division?
2. What are the differences between long division and synthetic division?
3. What are the advantages of synthetic division over long division?
4. Can synthetic division be used for all types of polynomial divisions?
5. How do you determine the quotient and remainder in polynomial division?

**Tip:** Synthetic division is especially efficient when dividing by a linear binomial like \(x - r\). It reduces the complexity by focusing only on the coefficients of the polynomial.

Divide the given polynomials and express the result in the form P(x)/D(x) = Q(x) + R(x)/D(x). Example provided: (x^4 + x^2 - 5) ÷ (x - 5).

Practice dividing polynomials using long division and synthetic division techniques. This activity includes step-by-step division of polynomials, including an example (x^4 + x^2 - 5) ÷ (x - 5). Suitable for students in Grades 10-12.

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