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 that the degree of polynomial AB is 15 and the degree of polynomial A is 5.

### Step-by-Step Solution:

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

2. **Assign Known Values**:
From the problem, we know:
- Degree of polynomial AB = 15
- Degree of polynomial A = 5
- Let the degree of polynomial B be denoted as \( d_B \).

3. **Set Up the Equation**:
Using the relationship from step 1, we can set up the equation:
\[ 15 = 5 + d_B \]

4. **Solve for \( d_B \)**:
To find \( d_B \), we can rearrange the equation:
\[ d_B = 15 - 5 \]
\[ d_B = 10 \]

5. **Conclusion**:
Therefore, the degree of polynomial B is 10.

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