Solve like example. This image illustrates the process of polynomial long division. The given expression is divided by \(x - 1\). The long division involves the following steps:1. **Division Set-Up**: - Dividend: \(x^3 + 3x^2 - 2x + 6\) - Divisor: \(x - 1\)2. **First Step**: - Divide the first term of the dividend (\(x^3\)) by the first term of the divisor (\(x\)) to get \(x^2\). - Multiply \(x^2\) by the divisor \(x - 1\), which gives \(x^3 - x^2\). - Subtract \(x^3 - x^2\) from the dividend to get a new dividend of \(4x^2 - 2x\).3. **Second Step**: - Divide the first term of the new dividend (\(4x^2\)) by the first term of the divisor (\(x\)) to get \(4x\). - Multiply \(4x\) by the divisor \(x - 1\), which gives \(4x^2 - 4x\). - Subtract \(4x^2 - 4x\) from the current dividend to get a new dividend of \(2x + 6\).4. **Third Step**: - Divide the first term of the new dividend (\(2x\)) by the first term of the divisor (\(x\)) to get \(2\). - Multiply \(2\) by the divisor \(x - 1\), which gives \(2x - 2\). - Subtract \(2x - 2\) from the current dividend to get the remainder \(8\).5. **Result**: - The quotient is \(x^2 + 4x + 2\). - The remainder is \(8\). The final expression is:\[ x^2 + 4x + 2 + \frac{8}{x-1} \] **Mathematics Problem: Polynomial Division****Problem Statement:**Divide \( 9x^2 + 6x \) by \( 3x \). Show or explain how you got your answer.**Solution Explanation:**To divide the polynomial \( 9x^2 + 6x \) by \( 3x \), follow these steps:1. **Divide Each Term:** - **First Term:** \[ \frac{9x^2}{3x} = 3x \] - **Second Term:** \[ \frac{6x}{3x} = 2 \]2. **Combine the Results:** - The division yields: \[ 3x + 2 \]Therefore, the result of dividing \( 9x^2 + 6x \) by \( 3x \) is \( 3x + 2 \).**Conclusion:**The division simplifies the polynomial to \( 3x + 2 \). The division process involves simplifying each term independently and then combining the simplified terms to get the final result.

Given query is to perform long division.

Answered: x³ + 3x²-2x+6 -x3+x² ↓ 4x² - 2x -4x²…

x³ + 3x²-2x+6 -x3+x² ↓ 4x² - 2x -4x² ±4x 2x +6 -2x=2 8 Quotient: x2 + 4x + 2 + 8 X-1

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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