Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### 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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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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