Long division. The question that is already asnwered is an example. Solve the blank question like the example. **Question**Divide by demonstrating the process of long division:Then answer the questions below:\[\frac{6x^3 + x^2 + 3x + 7}{3x - 4}\]1. State the quotient: ______________________________________________2. Is \(3x - 4\) a factor of \(6x^3 + x^2 + 3x + 7\)? ________________________3. Explain how you determined whether or not it is a factor. Title: Polynomial Long DivisionOn this educational page, we explore the polynomial long division method using an example division problem.### Example Problem:We have a dividend of \( 2x^3 - 13x^2 - x + 3 \) that we divide by the divisor \( 2x + 1 \).#### Steps:1. **First Term Division:** - Divide the leading term of the dividend \( 2x^3 \) by the leading term of the divisor \( 2x \), which gives \( x^2 \). - Calculation: \( \frac{2x^3}{2x} = x^2 \). - Multiply the entire divisor \( 2x + 1 \) by \( x^2 \) to get \( 2x^3 + x^2 \).2. **Subtract and Bring Down:** - Subtract \( 2x^3 + x^2 \) from the original dividend to get \(-14x^2 - x\). - Bring down the next term from the dividend to get \(-14x^2 - x\).3. **Second Term Division:** - Divide \(-14x^2 \) by the leading term of the divisor \( 2x \), which gives \(-7x\). - Calculation: \( \frac{-14x^2}{2x} = -7x \). - Multiply the entire divisor \( 2x + 1 \) by \(-7x\) to get \(-14x^2 - 7x\).4. **Subtract and Bring Down:** - Subtract \(-14x^2 - 7x\) from the current dividend to get \(6x + 3\). - Bring down the next term to get the new expression \(6x + 3\).5. **Third Term Division:** - Divide \(6x\) by the leading term of the divisor \(2x\), which gives \(3\). - Calculation: \( \frac{6x}{2x} = 3 \). - Multiply the entire divisor \(2x + 1\) by \(3\) to get \(6x + 3\).6. **Subtract:** - Subtract \(6x + 3\) from the current expression to get

Answered: Divide by demonstrating the process of…

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Algebra

Divide by demonstrating the process of long division: Then answer the questions below: 6x³ + x² + 3x + 7 3x - 4

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Long division. The question that is already asnwered is an example. Solve the blank question like the example.

**Question**

Divide by demonstrating the process of long division:

Then answer the questions below:

\[
\frac{6x^3 + x^2 + 3x + 7}{3x - 4}
\]

1. State the quotient: ______________________________________________

2. Is \(3x - 4\) a factor of \(6x^3 + x^2 + 3x + 7\)? ________________________

3. Explain how you determined whether or not it is a factor.

Title: Polynomial Long Division

On this educational page, we explore the polynomial long division method using an example division problem.

### Example Problem:

We have a dividend of \( 2x^3 - 13x^2 - x + 3 \) that we divide by the divisor \( 2x + 1 \).

#### Steps:

1. **First Term Division:**
- Divide the leading term of the dividend \( 2x^3 \) by the leading term of the divisor \( 2x \), which gives \( x^2 \).
- Calculation: \( \frac{2x^3}{2x} = x^2 \).
- Multiply the entire divisor \( 2x + 1 \) by \( x^2 \) to get \( 2x^3 + x^2 \).

2. **Subtract and Bring Down:**
- Subtract \( 2x^3 + x^2 \) from the original dividend to get \(-14x^2 - x\).
- Bring down the next term from the dividend to get \(-14x^2 - x\).

3. **Second Term Division:**
- Divide \(-14x^2 \) by the leading term of the divisor \( 2x \), which gives \(-7x\).
- Calculation: \( \frac{-14x^2}{2x} = -7x \).
- Multiply the entire divisor \( 2x + 1 \) by \(-7x\) to get \(-14x^2 - 7x\).

4. **Subtract and Bring Down:**
- Subtract \(-14x^2 - 7x\) from the current dividend to get \(6x + 3\).
- Bring down the next term to get the new expression \(6x + 3\).

5. **Third Term Division:**
- Divide \(6x\) by the leading term of the divisor \(2x\), which gives \(3\).
- Calculation: \( \frac{6x}{2x} = 3 \).
- Multiply the entire divisor \(2x + 1\) by \(3\) to get \(6x + 3\).

6. **Subtract:**
- Subtract \(6x + 3\) from the current expression to get

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