Question

Match the degree to each polynomial
7x^5y^3
-6mn^2
5e^8f^6g
4x^7+3x4^4+6x^2
1.7
2.3
3.8
4.15

Answer 1

To find the degree of each polynomial, we need to determine the highest sum of the exponents of the variables in each term.

1. **For the polynomial \(7x^5y^3\)**:
- The degree is \(5 + 3 = 8\).
- **Match: 3. 8**

2. **For the polynomial \(-6mn^2\)**:
- The degree is \(1 + 2 = 3\).
- **Match: 2. 3**

3. **For the polynomial \(5e^8f^6g\)**:
- The degree is \(8 + 6 + 1 = 15\) (note that \(g\) has an exponent of 1).
- **Match: 4. 15**

4. **For the polynomial \(4x^7 + 3x^4 + 6x^2\)**:
- The highest degree term is \(4x^7\), so the degree is \(7\).
- **Match: 1. 7**

In summary, the matches are:
- \(7x^5y^3\) → **3. 8**
- \(-6mn^2\) → **2. 3**
- \(5e^8f^6g\) → **4. 15**
- \(4x^7 + 3x^4 + 6x^2\) → **1. 7**