Find the quotient for 4m^3-38m^2+57m-72/m-8 using long division. Clearly indicate your quotient with any remainders. Example attached, solve like example.
Find the quotient for 4m^3-38m^2+57m-72/m-8 using long division. Clearly indicate your quotient with any remainders. Example attached, solve like example.
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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Find the quotient for 4m^3-38m^2+57m-72/m-8 using long division. Clearly indicate your quotient with any remainders. Example attached, solve like example.
![This image displays the process of polynomial long division. The dividend is \(x^2 - 3x + 2\) and the divisor is \(3x + 9\).
### Steps:
1. **Initial Setup**:
- The term \(3x^3 + 0x^2 + 4x + 11\) is divided by the first term of the divisor, \(3x\).
- The quotient begins with \(3x\).
2. **First Multiplication and Subtraction**:
- Multiply \(3x\) by the divisor \(3x + 9\) resulting in \(3x^3 + 9x^2\).
- Subtract from the current dividend:
\[
(3x^3 + 0x^2 + 4x + 11) - (3x^3 + 9x^2) = -9x^2 + 4x + 11
\]
3. **Next Step**:
- Bring down the next term to get \(-9x^2 + 4x + 11\).
- Divide \(-9x^2\) by \(3x\) to get \(-3x\).
- Multiply \(-3x\) by the divisor to get \(-9x^2 - 27x\).
4. **Subtraction**:
- Subtract:
\[
(-9x^2 + 4x + 11) - (-9x^2 - 27x) = 31x + 11
\]
5. **Final Division**:
- Divide \(31x\) by \(3x\) to get the next term of the quotient.
- Continue the process as necessary.
### Result:
- The quotient of the division is written as:
\[
\text{Quotient: } 3x + 9 + \frac{25x - 7}{x^2-3x+2}
\]
This process describes how to carry out each step of polynomial long division with detailed subtractions and calculations, clearly showing the development of the quotient.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f1dea97-750a-4100-b549-29ad8edbee52%2F8abc281f-5085-41ae-988e-3f44e6c2c3e6%2Fwczq8p_processed.png&w=3840&q=75)
Transcribed Image Text:This image displays the process of polynomial long division. The dividend is \(x^2 - 3x + 2\) and the divisor is \(3x + 9\).
### Steps:
1. **Initial Setup**:
- The term \(3x^3 + 0x^2 + 4x + 11\) is divided by the first term of the divisor, \(3x\).
- The quotient begins with \(3x\).
2. **First Multiplication and Subtraction**:
- Multiply \(3x\) by the divisor \(3x + 9\) resulting in \(3x^3 + 9x^2\).
- Subtract from the current dividend:
\[
(3x^3 + 0x^2 + 4x + 11) - (3x^3 + 9x^2) = -9x^2 + 4x + 11
\]
3. **Next Step**:
- Bring down the next term to get \(-9x^2 + 4x + 11\).
- Divide \(-9x^2\) by \(3x\) to get \(-3x\).
- Multiply \(-3x\) by the divisor to get \(-9x^2 - 27x\).
4. **Subtraction**:
- Subtract:
\[
(-9x^2 + 4x + 11) - (-9x^2 - 27x) = 31x + 11
\]
5. **Final Division**:
- Divide \(31x\) by \(3x\) to get the next term of the quotient.
- Continue the process as necessary.
### Result:
- The quotient of the division is written as:
\[
\text{Quotient: } 3x + 9 + \frac{25x - 7}{x^2-3x+2}
\]
This process describes how to carry out each step of polynomial long division with detailed subtractions and calculations, clearly showing the development of the quotient.
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