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

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

Algebra and Trigonometry (6th Edition)
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.
Transcribed Image Text:**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
Transcribed Image Text: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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