Question
Question 3
Sort the terms and their examples
A card sort is on the screen. To start dragging a card, Tab to it and press M to mark it. Next, Tab to the card where you want to drop, and press J to join the two cards together. To unjoin the selected card from a group, press U.
1
2x5−x3−9
8
2x+7x−5
x
1
2+15x3
1
2x−5−x3−9
2x4+3x
Sort the terms and their examples
A card sort is on the screen. To start dragging a card, Tab to it and press M to mark it. Next, Tab to the card where you want to drop, and press J to join the two cards together. To unjoin the selected card from a group, press U.
1
2x5−x3−9
8
2x+7x−5
x
1
2+15x3
1
2x−5−x3−9
2x4+3x
Answers
GPT-4o mini
To sort the given expressions, we can categorize them based on their degree and other characteristics. Here’s the breakdown of the terms and their examples:
### Sorted by Degree
1. **Degree 0** (Constant term)
- \( 8 \)
2. **Degree 1** (Linear term)
- \( x \)
3. **Degree 2** (Quadratic term)
- \( 2x + 7x - 5 \) (which can be simplified to \( 9x - 5 \))
4. **Degree 3** (Cubic term)
- \( \frac{1}{2} + 15x^3 \)
- \( -x^3 - 9 \) (part of expressions, but not a stand-alone term)
5. **Degree 4** (Quartic term)
- \( 2x^4 + 3x \)
6. **Degree 5** (Quintic term)
- \( 2x^5 - x^3 - 9 \) \( \Rightarrow \) Note that this expression contains a mix of terms, but it has \( x^5 \) as the highest degree.
7. **Mixed Expression**
- \( \frac{1}{2}x - 5 - x^3 - 9 \) (contains multiple degrees)
### Summary of the Sorted Terms
- **Constant**: \( 8 \)
- **Linear**: \( x \)
- **Quadratic**: \( 9x - 5 \)
- **Cubic**: \( \frac{1}{2} + 15x^3 \), \( -x^3 - 9 \)
- **Quartic**: \( 2x^4 + 3x \)
- **Quintic**: \( 2x^5 - x^3 - 9 \)
- **Mixed**: \( \frac{1}{2}x - 5 - x^3 - 9 \)
Feel free to ask if you need further assistance or details!
### Sorted by Degree
1. **Degree 0** (Constant term)
- \( 8 \)
2. **Degree 1** (Linear term)
- \( x \)
3. **Degree 2** (Quadratic term)
- \( 2x + 7x - 5 \) (which can be simplified to \( 9x - 5 \))
4. **Degree 3** (Cubic term)
- \( \frac{1}{2} + 15x^3 \)
- \( -x^3 - 9 \) (part of expressions, but not a stand-alone term)
5. **Degree 4** (Quartic term)
- \( 2x^4 + 3x \)
6. **Degree 5** (Quintic term)
- \( 2x^5 - x^3 - 9 \) \( \Rightarrow \) Note that this expression contains a mix of terms, but it has \( x^5 \) as the highest degree.
7. **Mixed Expression**
- \( \frac{1}{2}x - 5 - x^3 - 9 \) (contains multiple degrees)
### Summary of the Sorted Terms
- **Constant**: \( 8 \)
- **Linear**: \( x \)
- **Quadratic**: \( 9x - 5 \)
- **Cubic**: \( \frac{1}{2} + 15x^3 \), \( -x^3 - 9 \)
- **Quartic**: \( 2x^4 + 3x \)
- **Quintic**: \( 2x^5 - x^3 - 9 \)
- **Mixed**: \( \frac{1}{2}x - 5 - x^3 - 9 \)
Feel free to ask if you need further assistance or details!