Match the degree to each polynomial

Question

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