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Use synthetic division to find the quotient and remainder when 6x° – 2x* + 9x² + 9 is divided by x- 2. The quotient is . The remainder is.

Use synthetic division to find the quotient and remainder when 6x° – 2x* + 9x² + 9 is divided by x- 2. The quotient is . The remainder is.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Synthetic Division Example **Problem Statement:** Use synthetic division to find the quotient and remainder when \(8x^6 - 4x^4 + 3x^2 + 6\) is divided by \(x - 2\). **Solution:** - **The quotient is:** \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\). - **The remainder is:** 466. **Feedback:** Your solution was marked incorrect. - **Correct answers:** - Quotient: \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\) - Remainder: 466 - **Your answers:** - Quotient: \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\) - Remainder: \(x - 2\) **Explanation:** - The correct remainder is a constant: 466, not \(x - 2\). **Options:** - You can choose to attempt a similar question or proceed to the next question.
Transcribed Image Text:### Synthetic Division Example **Problem Statement:** Use synthetic division to find the quotient and remainder when \(8x^6 - 4x^4 + 3x^2 + 6\) is divided by \(x - 2\). **Solution:** - **The quotient is:** \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\). - **The remainder is:** 466. **Feedback:** Your solution was marked incorrect. - **Correct answers:** - Quotient: \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\) - Remainder: 466 - **Your answers:** - Quotient: \(8x^5 + 16x^4 + 28x^3 + 56x^2 + 115x + 230\) - Remainder: \(x - 2\) **Explanation:** - The correct remainder is a constant: 466, not \(x - 2\). **Options:** - You can choose to attempt a similar question or proceed to the next question.
**Synthetic Division of Polynomials** **Problem:** Use synthetic division to find the quotient and remainder when \(6x^6 - 2x^4 + 9x^2 + 9\) is divided by \(x - 2\). **Steps to solve:** 1. Write down the coefficients of the polynomial: - \(6, 0, -2, 0, 9, 0, 9\) 2. Use synthetic division with the divisor \(x - 2\). The value used for synthetic division is \(2\). 3. Set up the synthetic division: \[ \begin{array}{c|ccccccc} 2 & 6 & 0 & -2 & 0 & 9 & 0 & 9 \\ & & 12 & 24 & 44 & 88 & 194 & 388\\ \hline & 6 & 12 & 22 & 44 & 97 & 194 & 397 \\ \end{array} \] **Explanation of Diagram:** - The first row under the line are the initial coefficients. - The second row is the result of each step, where each entry is obtained by multiplying the previous result by 2 and adding it to the next coefficient. - The bottom row gives the coefficients of the quotient polynomial, and the final number is the remainder. **Result:** - The quotient is \(6x^5 + 12x^4 + 22x^3 + 44x^2 + 97x + 194\). - The remainder is \(397\). **Conclusion:** - The polynomial \(6x^6 - 2x^4 + 9x^2 + 9\) divided by \(x - 2\) gives a quotient \(6x^5 + 12x^4 + 22x^3 + 44x^2 + 97x + 194\) with a remainder of \(397\).
Transcribed Image Text:**Synthetic Division of Polynomials** **Problem:** Use synthetic division to find the quotient and remainder when \(6x^6 - 2x^4 + 9x^2 + 9\) is divided by \(x - 2\). **Steps to solve:** 1. Write down the coefficients of the polynomial: - \(6, 0, -2, 0, 9, 0, 9\) 2. Use synthetic division with the divisor \(x - 2\). The value used for synthetic division is \(2\). 3. Set up the synthetic division: \[ \begin{array}{c|ccccccc} 2 & 6 & 0 & -2 & 0 & 9 & 0 & 9 \\ & & 12 & 24 & 44 & 88 & 194 & 388\\ \hline & 6 & 12 & 22 & 44 & 97 & 194 & 397 \\ \end{array} \] **Explanation of Diagram:** - The first row under the line are the initial coefficients. - The second row is the result of each step, where each entry is obtained by multiplying the previous result by 2 and adding it to the next coefficient. - The bottom row gives the coefficients of the quotient polynomial, and the final number is the remainder. **Result:** - The quotient is \(6x^5 + 12x^4 + 22x^3 + 44x^2 + 97x + 194\). - The remainder is \(397\). **Conclusion:** - The polynomial \(6x^6 - 2x^4 + 9x^2 + 9\) divided by \(x - 2\) gives a quotient \(6x^5 + 12x^4 + 22x^3 + 44x^2 + 97x + 194\) with a remainder of \(397\).
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