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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Question
factor each problem and choose the answer from the bottom options
![The image contains a list of quadratic equations with spaces to input their factors, alongside their solutions. Below the equations, there is a selection of possible factors and solutions.
### Quadratic Equations and Their Solutions:
1. **Equation**: \(9x^2 + 6x - 8 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-\frac{4}{3}, \frac{2}{3}\right\}\)
2. **Equation**: \(x^2 + 2x + 1 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{-1\}\)
3. **Equation**: \(x^2 + 2x - 48 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{-8, 6\}\)
4. **Equation**: \(3x^2 + 7x - 6 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-3, \frac{2}{3}\right\}\)
5. **Equation**: \(2x^2 - 32x + 96 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{4, 12\}\)
6. **Equation**: \(5x^2 + 2x = 3\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-1, \frac{3}{5}\right\}\)
### Potential Factors and Solutions:
- Possible factors include various linear expressions such as \(x+4\), \(3x+4\), \(x+6\), \(3x-2\), \(x+1\), etc.
- Provided solutions include sets of numbers like \(\{-1, \frac{3}{5}\}\), \(\left\{-\frac{4}{3}, \frac{2}{3}\right\}\), and others.
Students are expected to match the correct factors to the quadratic equations based on their solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed42ece2-097d-4a8d-86d6-76a5b3cf85d0%2F01f49ba8-e7d6-43ad-84fd-4d4f5cb0bcee%2Ftkqdwnx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a list of quadratic equations with spaces to input their factors, alongside their solutions. Below the equations, there is a selection of possible factors and solutions.
### Quadratic Equations and Their Solutions:
1. **Equation**: \(9x^2 + 6x - 8 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-\frac{4}{3}, \frac{2}{3}\right\}\)
2. **Equation**: \(x^2 + 2x + 1 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{-1\}\)
3. **Equation**: \(x^2 + 2x - 48 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{-8, 6\}\)
4. **Equation**: \(3x^2 + 7x - 6 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-3, \frac{2}{3}\right\}\)
5. **Equation**: \(2x^2 - 32x + 96 = 0\)
**Factors**: [Space for factors]
**Solution**: \(\{4, 12\}\)
6. **Equation**: \(5x^2 + 2x = 3\)
**Factors**: [Space for factors]
**Solution**: \(\left\{-1, \frac{3}{5}\right\}\)
### Potential Factors and Solutions:
- Possible factors include various linear expressions such as \(x+4\), \(3x+4\), \(x+6\), \(3x-2\), \(x+1\), etc.
- Provided solutions include sets of numbers like \(\{-1, \frac{3}{5}\}\), \(\left\{-\frac{4}{3}, \frac{2}{3}\right\}\), and others.
Students are expected to match the correct factors to the quadratic equations based on their solutions.
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