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Use synthetic division to determine the quotient of (3x² – 17x − 28) ÷ (x-7). Show all your work in the sketch box. Sorties Remember to check for missing terms. Is x - 7 a factor of the dividend? yes no

Use synthetic division to determine the quotient of (3x² – 17x − 28) ÷ (x-7). Show all your work in the sketch box. Sorties Remember to check for missing terms. Is x - 7 a factor of the dividend? yes no

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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The image with a 1 on it is the question. The other image is an example of how to solve using synthetic division.

**Problem 1: Synthetic Division** Use synthetic division to determine the quotient of \( (3x^2 - 17x - 28) \div (x - 7) \). Show all your work in the sketch box. Remember to check for missing terms. **Question:** Is \( x - 7 \) a factor of the dividend? - [ ] yes - [ ] no Note: The area below the main problem is crossed out in blue, obscuring any additional instructions or information that may have been included there.
Transcribed Image Text:**Problem 1: Synthetic Division** Use synthetic division to determine the quotient of \( (3x^2 - 17x - 28) \div (x - 7) \). Show all your work in the sketch box. Remember to check for missing terms. **Question:** Is \( x - 7 \) a factor of the dividend? - [ ] yes - [ ] no Note: The area below the main problem is crossed out in blue, obscuring any additional instructions or information that may have been included there.
The image provides a step-by-step solution to dividing the polynomial \( \frac{3x^2 - 17x + 20}{x - 4} \) using polynomial long division. **Steps Explained:** 1. **Setup:** - The division problem: \(\frac{3x^2 - 17x + 20}{x - 4}\). - Identify the divisor \(x - 4\) and find the zero: \(x - 4 = 0 \Rightarrow x = 4\). 2. **Long Division Steps:** - Divide the first term of the dividend \(3x^2\) by the first term of the divisor \(x\) resulting in \(3x\). - Multiply \(3x\) by \(x - 4\), yielding \(3x^2 - 12x\). - Subtract \((3x^2 - 12x)\) from \((3x^2 - 17x)\) to get \(-5x\). - Bring down the next term, \(+20\). 3. **Repeat the Process:** - Divide \(-5x\) by \(x\) resulting in \(-5\). - Multiply \(-5\) by \(x - 4\), yielding \(-5x + 20\). - Subtract \((-5x + 20)\) from \((-5x + 20)\) to get a remainder of \(0\). 4. **Conclusion and Verification:** - The quotient is \(3x - 5\). - Since the remainder is \(0\), \(3x - 5\) and \(x - 4\) are factors of the dividend \(3x^2 - 17x + 20\). - Verification: \((3x - 5)(x - 4) = 3x^2 - 17x + 20\). This explanation covers polynomial long division, showing both the process and how to confirm the result.
Transcribed Image Text:The image provides a step-by-step solution to dividing the polynomial \( \frac{3x^2 - 17x + 20}{x - 4} \) using polynomial long division. **Steps Explained:** 1. **Setup:** - The division problem: \(\frac{3x^2 - 17x + 20}{x - 4}\). - Identify the divisor \(x - 4\) and find the zero: \(x - 4 = 0 \Rightarrow x = 4\). 2. **Long Division Steps:** - Divide the first term of the dividend \(3x^2\) by the first term of the divisor \(x\) resulting in \(3x\). - Multiply \(3x\) by \(x - 4\), yielding \(3x^2 - 12x\). - Subtract \((3x^2 - 12x)\) from \((3x^2 - 17x)\) to get \(-5x\). - Bring down the next term, \(+20\). 3. **Repeat the Process:** - Divide \(-5x\) by \(x\) resulting in \(-5\). - Multiply \(-5\) by \(x - 4\), yielding \(-5x + 20\). - Subtract \((-5x + 20)\) from \((-5x + 20)\) to get a remainder of \(0\). 4. **Conclusion and Verification:** - The quotient is \(3x - 5\). - Since the remainder is \(0\), \(3x - 5\) and \(x - 4\) are factors of the dividend \(3x^2 - 17x + 20\). - Verification: \((3x - 5)(x - 4) = 3x^2 - 17x + 20\). This explanation covers polynomial long division, showing both the process and how to confirm the result.
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