Question
Find the number of terms and the degree of this polynomial.
8y^2 - 7y^2 + 10y
8y^2 - 7y^2 + 10y
Answers
GPT-4o mini
To analyze the given polynomial \(8y^2 - 7y^2 + 10y\), we will first simplify it and then identify the number of terms and the degree.
1. **Combine Like Terms**:
- The terms \(8y^2\) and \(-7y^2\) can be combined:
\[
8y^2 - 7y^2 = 1y^2 = y^2
\]
- Therefore, the polynomial simplifies to:
\[
y^2 + 10y
\]
2. **Identify the Polynomial's Terms**:
- The simplified polynomial \(y^2 + 10y\) has two terms: \(y^2\) and \(10y\).
3. **Determine the Degree**:
- The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of \(y\) is 2 (from the term \(y^2\)).
**Conclusion**:
- The number of terms in the polynomial is **2**.
- The degree of the polynomial is **2**.
1. **Combine Like Terms**:
- The terms \(8y^2\) and \(-7y^2\) can be combined:
\[
8y^2 - 7y^2 = 1y^2 = y^2
\]
- Therefore, the polynomial simplifies to:
\[
y^2 + 10y
\]
2. **Identify the Polynomial's Terms**:
- The simplified polynomial \(y^2 + 10y\) has two terms: \(y^2\) and \(10y\).
3. **Determine the Degree**:
- The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of \(y\) is 2 (from the term \(y^2\)).
**Conclusion**:
- The number of terms in the polynomial is **2**.
- The degree of the polynomial is **2**.