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 7 of 9
**Select the correct statements from the table.**
For each expression, select the true statement in the table.
| Expression | Statement 1 | Statement 2 |
|--------------------------------------|-------------|--------------------------------------|
| \(4x^3 - 7x + 2 \over 4\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 3 terms. |
| {-\[3x^5 + 4x - 6\] \over \[2x^2 - 5\]} | This is a rational expression because the denominator contains a variable. | This is a polynomial with 4 terms. |
| \((7x^2 + 3)(5x + 1)\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 4 terms. |
| {9x^2 - 6x + 1 \over 5x + 7} | This is a rational expression because the denominator contains a variable. | This is a polynomial with 3 terms. |
| \(8x^4 - x^3 + 6x^2 - 3x + 9\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 5 terms. |
### Explanation:
1. **Expression \(4x^3 - 7x + 2 \over 4\)**:
- Statement 1: **Incorrect**, because the denominator \(4\) does not contain a variable.
- Statement 2: **Correct**, because the numerator \(4x^3 - 7x + 2\) is a polynomial with 3 terms.
2. **Expression \(3x^5 + 4x - 6 \over 2x^2 - 5\)**:
- Statement 1: **Correct**, because the denominator \(2x^2 - 5\) contains a variable.
- Statement 2: **Incorrect**, because it is a rational expression with a polynomial numerator and numerator with 3 terms.
3. **Expression \((7x^2 + 3)(5x + 1)\)**:
- Statement 1: **Incorrect**, because it is a single polynomial expression with no denominator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18451349-f722-4343-9ced-dbc580baaa92%2F59ec6938-bbab-4357-a385-421d416a4f80%2Fepzewci_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 7 of 9
**Select the correct statements from the table.**
For each expression, select the true statement in the table.
| Expression | Statement 1 | Statement 2 |
|--------------------------------------|-------------|--------------------------------------|
| \(4x^3 - 7x + 2 \over 4\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 3 terms. |
| {-\[3x^5 + 4x - 6\] \over \[2x^2 - 5\]} | This is a rational expression because the denominator contains a variable. | This is a polynomial with 4 terms. |
| \((7x^2 + 3)(5x + 1)\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 4 terms. |
| {9x^2 - 6x + 1 \over 5x + 7} | This is a rational expression because the denominator contains a variable. | This is a polynomial with 3 terms. |
| \(8x^4 - x^3 + 6x^2 - 3x + 9\) | This is a rational expression because the denominator contains a variable. | This is a polynomial with 5 terms. |
### Explanation:
1. **Expression \(4x^3 - 7x + 2 \over 4\)**:
- Statement 1: **Incorrect**, because the denominator \(4\) does not contain a variable.
- Statement 2: **Correct**, because the numerator \(4x^3 - 7x + 2\) is a polynomial with 3 terms.
2. **Expression \(3x^5 + 4x - 6 \over 2x^2 - 5\)**:
- Statement 1: **Correct**, because the denominator \(2x^2 - 5\) contains a variable.
- Statement 2: **Incorrect**, because it is a rational expression with a polynomial numerator and numerator with 3 terms.
3. **Expression \((7x^2 + 3)(5x + 1)\)**:
- Statement 1: **Incorrect**, because it is a single polynomial expression with no denominator.
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