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Find the quotient and remainder using long division. 9x + 3x2 + 22x 3x2 + 3

Find the quotient and remainder using long division. 9x + 3x2 + 22x 3x2 + 3

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 for Polynomials #### Problem 9: Find the quotient and remainder using long division. Given: \[ \frac{9x^3 + 3x^2 + 22x}{3x^2 + 3} \] ### Steps: 1. **Enter the Dividend and Divisor:** - Dividend: \(9x^3 + 3x^2 + 22x\) - Divisor: \(3x^2 + 3\) 2. **Division Process:** - Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient. - Multiply the entire divisor by this term and subtract the result from the dividend. - Repeat the process with the resulting polynomial. 3. **Result:** - Upon completing the above steps, you will obtain the quotient and remainder. ### Solution Boxes: - **Quotient:** [Input Box] - **Remainder:** [Input Box] --- ### Optional Step for Detailed Work: - **Show My Work (Optional):** [Expandable section to input detailed long division steps] ### Submit Answer - **Button:** [Submit Answer] ### Visual Explanation: There is no visual graph or diagram in this problem. The exercise focuses on polynomial long division, which involves breaking down the division process step-by-step. --- This setup guides the student through the process of long division with polynomials, encouraging them to find the quotient and remainder manually before submitting their answer for evaluation.
Transcribed Image Text:### Long Division for Polynomials #### Problem 9: Find the quotient and remainder using long division. Given: \[ \frac{9x^3 + 3x^2 + 22x}{3x^2 + 3} \] ### Steps: 1. **Enter the Dividend and Divisor:** - Dividend: \(9x^3 + 3x^2 + 22x\) - Divisor: \(3x^2 + 3\) 2. **Division Process:** - Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient. - Multiply the entire divisor by this term and subtract the result from the dividend. - Repeat the process with the resulting polynomial. 3. **Result:** - Upon completing the above steps, you will obtain the quotient and remainder. ### Solution Boxes: - **Quotient:** [Input Box] - **Remainder:** [Input Box] --- ### Optional Step for Detailed Work: - **Show My Work (Optional):** [Expandable section to input detailed long division steps] ### Submit Answer - **Button:** [Submit Answer] ### Visual Explanation: There is no visual graph or diagram in this problem. The exercise focuses on polynomial long division, which involves breaking down the division process step-by-step. --- This setup guides the student through the process of long division with polynomials, encouraging them to find the quotient and remainder manually before submitting their answer for evaluation.
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