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Fill in the missing values below one at a time to find the dividend when 2x³-11x6 is divided by x + 2. 2x² 2x³ +2 try You must answer all questions above in order to submit. atter 8 4x²

Fill in the missing values below one at a time to find the dividend when 2x³-11x6 is divided by x + 2. 2x² 2x³ +2 try You must answer all questions above in order to submit. atter 8 4x²

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter6: Polynomials
Section6.1: Add And Subtract Polynomials
Problem 85E: Using your own words, explain the difference between a polynomial with five terms and a polynomial...
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Question
### Polynomial Long Division Practice **Objective:** Fill in the missing values below one at a time to find the dividend when \( 2x^3 - 11x - 6 \) is divided by \( x + 2 \). #### Step-by-Step Instructions: 1. **Set up the long division:** - **Dividend:** \( 2x^3 - 11x - 6 \) - **Divisor:** \( x + 2 \) The division process starts by dividing the leading term of the dividend by the leading term of the divisor. 2. **Place the first term in the quotient:** - Divide \( 2x^3 \) by \( x \) to get \( 2x^2 \). #### Fill in the missing terms in the grid below: | | \( 2x^2 \) | | |---------|------------|-----------| | \( x \) | \( 2x^3 \) | | | \( +2 \)| \( 4x^2 \) | | #### Understanding the Diagram: - The top left box contains the term \( 2x^2 \), which is the result of the first division step. - The box directly beneath it contains \( 2x^3 \), which is the product of \( 2x^2 \) (from the quotient) and \( x \) (from the divisor). - The bottom right corner box contains \( 4x^2 \), which is the product of \( 2x^2 \) (from the quotient) and \( 2 \) (from the divisor). #### Next Steps: - Subtract \( 2x^3 + 4x^2 \) from \( 2x^3 - 11x - 6 \). - Continue the process by bringing down the next term and repeating the steps until the remainder is found or until there are no more terms to bring down. Finally, click on the "try" button to check your answer. **Note:** You must answer all questions above in order to submit your response. --- By following this detailed step-by-step explanation, students can gain a deeper understanding of polynomial long division, reinforcing their algebra skills and ensuring they are well-prepared for more advanced topics.
Transcribed Image Text:### Polynomial Long Division Practice **Objective:** Fill in the missing values below one at a time to find the dividend when \( 2x^3 - 11x - 6 \) is divided by \( x + 2 \). #### Step-by-Step Instructions: 1. **Set up the long division:** - **Dividend:** \( 2x^3 - 11x - 6 \) - **Divisor:** \( x + 2 \) The division process starts by dividing the leading term of the dividend by the leading term of the divisor. 2. **Place the first term in the quotient:** - Divide \( 2x^3 \) by \( x \) to get \( 2x^2 \). #### Fill in the missing terms in the grid below: | | \( 2x^2 \) | | |---------|------------|-----------| | \( x \) | \( 2x^3 \) | | | \( +2 \)| \( 4x^2 \) | | #### Understanding the Diagram: - The top left box contains the term \( 2x^2 \), which is the result of the first division step. - The box directly beneath it contains \( 2x^3 \), which is the product of \( 2x^2 \) (from the quotient) and \( x \) (from the divisor). - The bottom right corner box contains \( 4x^2 \), which is the product of \( 2x^2 \) (from the quotient) and \( 2 \) (from the divisor). #### Next Steps: - Subtract \( 2x^3 + 4x^2 \) from \( 2x^3 - 11x - 6 \). - Continue the process by bringing down the next term and repeating the steps until the remainder is found or until there are no more terms to bring down. Finally, click on the "try" button to check your answer. **Note:** You must answer all questions above in order to submit your response. --- By following this detailed step-by-step explanation, students can gain a deeper understanding of polynomial long division, reinforcing their algebra skills and ensuring they are well-prepared for more advanced topics.
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