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You have uploaded an image with polynomial division problems using long division. Here’s a breakdown of the problems from the image:

### Divide using long division:

1. \( \left( x^3 + 8x^2 - 3x + 16 \right) \div (x + 5) \)
2. \( \left( 4x^2 + 5x + 8 \right) \div (x + 1) \)
3. \( \left( x^3 - 14x + 8 \right) \div (x + 4) \)
4. \( \left( x^2 + 10 \right) \div (x + 4) \)
5. \( \left( 10x^4 + 5x^3 + 4x^2 - 9 \right) \div (x + 1) \)

Let me know if you’d like a detailed solution for any of these problems or all of them!

Here are five questions to expand on this content:

1. What is the remainder in polynomial division, and how does it affect the final result?
2. Can synthetic division be used for any of these problems instead of long division?
3. How would you verify if a quotient is correct after performing long division?
4. What are the applications of polynomial division in real-world problems?
5. How does dividing by a binomial like \(x + a\) differ from dividing by a higher-degree polynomial?

**Tip:** Always check the degree of the remainder after dividing polynomials; it should be less than the degree of the divisor.

Divide polynomials using long division as shown in the problems.

Learn how to divide polynomials using long division. This set includes problems such as dividing cubic and quadratic polynomials by binomials, covering key algebraic concepts for high school students in Grades 10-12.

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