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Bot GPT 4-o mini Let's evaluate each statement one by one:
1. **5a²b - 6ab³c + 3a⁵ is a fifth degree polynomial.**
- True. The highest degree of the terms is 5 from the term **3a⁵**.
2. **5a²b - 6ab³c + 3a⁵ has a leading coefficient of 5.**
- False. The leading term (the term with the highest degree) is **3a⁵**, which has a leading coefficient of 3, not 5.
3. **5a²b - 6ab³c + 3a⁵ contains three terms.**
- True. This polynomial contains three distinct terms: **5a²b**, **-6ab³c**, and **3a⁵**.
4. **12x - 10x⁵ - 7 + 3x⁴ has a leading coefficient of 12.**
- False. The leading term is **-10x⁵**, which has a leading coefficient of -10.
5. **12x - 10x⁵ - 7 + 3x⁴ is equivalent to -10x⁵ + 3x⁴ + 12x - 7.**
- True. This statement correctly represents the same polynomial rearranged.
6. **12x - 10x⁵ - 7 + 3x⁴ has a leading term of -10x⁵.**
- True. The leading term of this polynomial is indeed **-10x⁵**.
### Summary:
The true statements are:
- **5a²b - 6ab³c + 3a⁵ is a fifth degree polynomial.**
- **5a²b - 6ab³c + 3a⁵ contains three terms.**
- **12x - 10x⁵ - 7 + 3x⁴ is equivalent to -10x⁵ + 3x⁴ + 12x - 7.**
- **12x - 10x⁵ - 7 + 3x⁴ has a leading term of -10x⁵.**