The degree of a polyonial A is 7 and that of polynomial AB is 65, then find the degree of polynomial B

Answer

To find the degree of polynomial B given that the degree of polynomial A is 7 and the degree of the product polynomial AB is 65, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between degrees of polynomials**:
The degree of the product of two polynomials is equal to the sum of their degrees. This can be expressed as:
\[ \text{Degree}(AB) = \text{Degree}(A) + \text{Degree}(B) \]

2. **Identify the given values**:
From the question, we know:
- Degree of polynomial A, \(\text{Degree}(A) = 7\)
- Degree of polynomial AB, \(\text{Degree}(AB) = 65\)

3. **Set up the equation**:
Using the relationship from step 1, we can set up the equation:
\[ 65 = 7 + \text{Degree}(B) \]

4. **Solve for the degree of polynomial B**:
To find the degree of polynomial B, we can rearrange the equation:
\[ \text{Degree}(B) = 65 - 7 \]
\[ \text{Degree}(B) = 58 \]

5. **Conclusion**:
Therefore, the degree of polynomial B is \(58\).

### Final Answer:
The degree of polynomial B is **58**.