Question
Determine the degree of the polynomial \( -2y^{5} + y - 4y^{3} \).
Ask by Floyd Phillips. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The degree of the polynomial \( -2y^{5} + y - 4y^{3} \) is **5**.
Solution
To determine the **degree** of the polynomial \( -2y^{5} + y - 4y^{3} \), follow these steps:
1. **Identify Each Term and Its Degree:**
- **\( -2y^{5} \)**: The exponent of \( y \) is **5**.
- **\( y \)**: This term can be written as \( y^{1} \), so the exponent is **1**.
- **\( -4y^{3} \)**: The exponent of \( y \) is **3**.
2. **Determine the Highest Degree:**
- Among the exponents \( 5 \), \( 1 \), and \( 3 \), the highest is **5**.
3. **Conclusion:**
- The **degree** of the polynomial is **5**.
**Answer:** The degree of the polynomial \( -2y^{5} + y - 4y^{3} \) is **5**.
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Simplify this solution The Deep Dive
The degree of a polynomial is determined by the highest power of the variable in the polynomial. In the polynomial \( -2y^{5} + y - 4y^{3} \), we have three terms: 1. \( -2y^{5} \) has a degree of 5. 2. \( y \) (which is \( y^1 \)) has a degree of 1. 3. \( -4y^{3} \) has a degree of 3. The highest degree among these terms is \( 5 \). Therefore, the degree of the polynomial \( -2y^{5} + y - 4y^{3} \) is \( 5 \).
