If the degree of a polynomial AB is 15 and the degree of polynomial A is 5, then find the degree of polynomial B.

Answer

To solve the problem, we need to find the degree of polynomial B given the degree of polynomial AB and the degree of polynomial A.

### Step-by-Step Solution:

1. **Understand the given information**:
- The degree of polynomial AB is given as 15.
- The degree of polynomial A is given as 5.

2. **Use the formula for the degree of the product of two polynomials**:
- The degree of the product of two polynomials (AB) is equal to the sum of their degrees.
- Mathematically, this can be expressed as:
\[ \text{Degree of } AB = \text{Degree of } A + \text{Degree of } B \]

3. **Substitute the known values into the formula**:
- We know:
\[ \text{Degree of } AB = 15 \]
\[ \text{Degree of } A = 5 \]
- Therefore, we can write:
\[ 15 = 5 + \text{Degree of } B \]

4. **Solve for the degree of polynomial B**:
- Rearranging the equation gives:
\[ \text{Degree of } B = 15 - 5 \]
- Simplifying this results in:
\[ \text{Degree of } B = 10 \]

5. **Conclusion**:
- The degree of polynomial B is 10.

### Final Answer:
The degree of polynomial B is 10.