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Is x-7 a factor of the dividend?

Is x-7 a factor of the dividend?

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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Is x-7 a factor of the dividend?

The image depicts the polynomial long division of \((3x^2 - 17x - 28)\) by \((x - 7)\). **Explanation:** 1. **Divisor and Dividend:** The divisor is \(x - 7\), and the dividend is \(3x^2 - 17x - 28\). 2. **Division Process:** - First, divide the leading term of the dividend \(3x^2\) by the leading term of the divisor \(x\), resulting in \(3x\). - Multiply the entire divisor \(x - 7\) by \(3x\) to get \(3x^2 - 21x\). - Subtract \(3x^2 - 21x\) from the original dividend \(3x^2 - 17x - 28\) to get \(4x - 28\). 3. **Repeat Process:** - Divide the new leading term \(4x\) by the leading term of the divisor \(x\), resulting in \(4\). - Multiply the divisor \(x - 7\) by \(4\) to get \(4x - 28\). - Subtract \(4x - 28\) from \(4x - 28\) to get a remainder of \(0\). 4. **Conclusion:** - The quotient is \(3x - 4\) with a remainder of \(0\). The division process completes without a remainder, indicating that \((x - 7)\) is a factor of \((3x^2 - 17x - 28)\).
Transcribed Image Text:The image depicts the polynomial long division of \((3x^2 - 17x - 28)\) by \((x - 7)\). **Explanation:** 1. **Divisor and Dividend:** The divisor is \(x - 7\), and the dividend is \(3x^2 - 17x - 28\). 2. **Division Process:** - First, divide the leading term of the dividend \(3x^2\) by the leading term of the divisor \(x\), resulting in \(3x\). - Multiply the entire divisor \(x - 7\) by \(3x\) to get \(3x^2 - 21x\). - Subtract \(3x^2 - 21x\) from the original dividend \(3x^2 - 17x - 28\) to get \(4x - 28\). 3. **Repeat Process:** - Divide the new leading term \(4x\) by the leading term of the divisor \(x\), resulting in \(4\). - Multiply the divisor \(x - 7\) by \(4\) to get \(4x - 28\). - Subtract \(4x - 28\) from \(4x - 28\) to get a remainder of \(0\). 4. **Conclusion:** - The quotient is \(3x - 4\) with a remainder of \(0\). The division process completes without a remainder, indicating that \((x - 7)\) is a factor of \((3x^2 - 17x - 28)\).
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