Divide Using Long Division: $ (-2x^3 - 4x^2 - 4x + 2) \div (x - 4) }$Options A. { -2x^2 + 4x + 44, \text{ R 210$}$B. { -2x^2 - 12x - 52$}$C. { -2x^2 + 4x + 44$} D . \[ D. \[ D . \[ -2x^2 - 12x - 52, \text{ R }

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Introduction

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Long division is a mathematical technique used to divide a polynomial by another polynomial. It is an essential tool in algebra and is used to simplify complex expressions. In this article, we will focus on dividing a polynomial using long division, with a specific example of dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$.

Understanding Long Division

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Long division is a process of dividing a polynomial by another polynomial. It involves dividing the highest degree term of the dividend by the highest degree term of the divisor, and then multiplying the entire divisor by the result and subtracting it from the dividend. This process is repeated until the degree of the remainder is less than the degree of the divisor.

Step-by-Step Guide to Long Division

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To divide a polynomial using long division, follow these steps:

1. Write the dividend and divisor: Write the dividend and divisor in the correct format, with the dividend on top and the divisor on the bottom.
2. Divide the highest degree term: Divide the highest degree term of the dividend by the highest degree term of the divisor.
3. Multiply the divisor: Multiply the entire divisor by the result from step 2.
4. Subtract the product: Subtract the product from step 3 from the dividend.
5. Bring down the next term: Bring down the next term of the dividend.
6. Repeat the process: Repeat steps 2-5 until the degree of the remainder is less than the degree of the divisor.

Example: Dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$

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Let's use the example of dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$ to illustrate the long division process.

Step 1: Write the dividend and divisor

	$x - 4$
$-2x^3 - 4x^2 - 4x + 2$

Step 2: Divide the highest degree term

Divide the highest degree term of the dividend ($-2x^3$) by the highest degree term of the divisor ($x$). The result is $-2x^2$.

Step 3: Multiply the divisor

Multiply the entire divisor ($x - 4$) by the result from step 2 ($-2x^2$). The product is $-2x^3 + 8x^2$.

Step 4: Subtract the product

Subtract the product from step 3 ($-2x^3 + 8x^2$) from the dividend ($-2x^3 - 4x^2 - 4x + 2$). The result is $-12x^2 - 4x + 2$.

Step 5: Bring down the next term

Bring down the next term of the dividend ($-4x$).

Step 6: Repeat the process

Repeat steps 2-5 until the degree of the remainder is less than the degree of the divisor.

Step 7: Final result

After repeating the process, the final result is $-2x^2 + 4x + 44$, with a remainder of $210$.

Conclusion

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In conclusion, long division is a powerful tool in algebra that allows us to divide a polynomial by another polynomial. By following the step-by-step guide outlined in this article, we can divide a polynomial using long division. The example of dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$ illustrates the process of long division and provides a clear understanding of how to use this technique.

Answer

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The correct answer is:

• A. $-2x^2 + 4x + 44, \text{ R } 210$

This answer is based on the long division process outlined in this article. The remainder of $210$ is obtained by subtracting the product of the divisor and the result from the dividend.

Discussion

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The discussion category for this article is mathematics. This article provides a step-by-step guide to dividing a polynomial using long division, with a specific example of dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$. The article provides a clear understanding of how to use long division to simplify complex expressions.

Related Topics

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• Polynomial division: This article provides a step-by-step guide to dividing a polynomial using long division.
• Algebra: This article provides a clear understanding of how to use long division to simplify complex expressions.
• Mathematics: This article provides a discussion category for mathematics.

Key Takeaways

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• Long division: This article provides a step-by-step guide to dividing a polynomial using long division.
• Polynomial division: This article provides a clear understanding of how to use long division to simplify complex expressions.
• Algebra: This article provides a clear understanding of how to use long division to simplify complex expressions.

Conclusion

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In conclusion, long division is a powerful tool in algebra that allows us to divide a polynomial by another polynomial. By following the step-by-step guide outlined in this article, we can divide a polynomial using long division. The example of dividing $(-2x^3 - 4x^2 - 4x + 2)$ by $(x - 4)$ illustrates the process of long division and provides a clear understanding of how to use this technique.

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Introduction

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Long division is a mathematical technique used to divide a polynomial by another polynomial. It is an essential tool in algebra and is used to simplify complex expressions. In this article, we will answer some frequently asked questions (FAQs) about long division.

Q&A

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Q: What is long division?

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A: Long division is a mathematical technique used to divide a polynomial by another polynomial. It is an essential tool in algebra and is used to simplify complex expressions.

Q: How do I divide a polynomial using long division?

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A: To divide a polynomial using long division, follow these steps:

1. Write the dividend and divisor: Write the dividend and divisor in the correct format, with the dividend on top and the divisor on the bottom.
2. Divide the highest degree term: Divide the highest degree term of the dividend by the highest degree term of the divisor.
3. Multiply the divisor: Multiply the entire divisor by the result from step 2.
4. Subtract the product: Subtract the product from step 3 from the dividend.
5. Bring down the next term: Bring down the next term of the dividend.
6. Repeat the process: Repeat steps 2-5 until the degree of the remainder is less than the degree of the divisor.

Q: What is the remainder in long division?

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A: The remainder in long division is the amount left over after dividing the dividend by the divisor. It is the result of subtracting the product of the divisor and the result from the dividend.

Q: How do I know when to stop dividing?

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A: You know when to stop dividing when the degree of the remainder is less than the degree of the divisor. This means that you have divided the dividend by the divisor as many times as possible.

Q: Can I use long division to divide fractions?

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A: No, you cannot use long division to divide fractions. Long division is used to divide polynomials, not fractions.

Q: Can I use long division to divide decimals?

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A: No, you cannot use long division to divide decimals. Long division is used to divide polynomials, not decimals.

Q: What are some common mistakes to avoid when using long division?

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A: Some common mistakes to avoid when using long division include:

• Not writing the dividend and divisor in the correct format: Make sure to write the dividend and divisor in the correct format, with the dividend on top and the divisor on the bottom.
• Not dividing the highest degree term: Make sure to divide the highest degree term of the dividend by the highest degree term of the divisor.
• Not multiplying the divisor: Make sure to multiply the entire divisor by the result from step 2.
• Not subtracting the product: Make sure to subtract the product from step 3 from the dividend.
• Not bringing down the next term: Make sure to bring down the next term of the dividend.
• Not repeating the process: Make sure to repeat steps 2-5 until the degree of the remainder is less than the degree of the divisor.

Conclusion

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In conclusion, long division is a powerful tool in algebra that allows us to divide a polynomial by another polynomial. By following the step-by-step guide outlined in this article, we can divide a polynomial using long division. The FAQs provided in this article answer some common questions about long division and provide a clear understanding of how to use this technique.

Related Topics

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• Polynomial division: This article provides a step-by-step guide to dividing a polynomial using long division.
• Algebra: This article provides a clear understanding of how to use long division to simplify complex expressions.
• Mathematics: This article provides a discussion category for mathematics.

Key Takeaways

---

• Long division: This article provides a step-by-step guide to dividing a polynomial using long division.
• Polynomial division: This article provides a clear understanding of how to use long division to simplify complex expressions.
• Algebra: This article provides a clear understanding of how to use long division to simplify complex expressions.

Conclusion

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In conclusion, long division is a powerful tool in algebra that allows us to divide a polynomial by another polynomial. By following the step-by-step guide outlined in this article, we can divide a polynomial using long division. The FAQs provided in this article answer some common questions about long division and provide a clear understanding of how to use this technique.