Question

Answer the questions about the following polynomial.
9, x, to the power 5 , minus, 6, plus, one tenth, x, to the power 4
9x
5
−6+
10
1
​
x
4


The expression represents a _____ polynomial with ____terms. The constant term is
____, the leading term is _____, and the leading coefficient is___.

Answer 1

The given polynomial is \(9x^5 - 6 + \frac{1}{10}x^4\).

1. **Type of Polynomial**: The expression represents a **polynomial**.
2. **Number of Terms**: To count the number of terms, we identify the separate components:
- \(9x^5\)
- \(\frac{1}{10}x^4\)
- \(-6\)

This gives us a total of **3 terms**.

3. **Constant Term**: The constant term is the term without a variable, which is **\(-6\)**.

4. **Leading Term**: The leading term is the term with the highest degree, which is **\(9x^5\)**.

5. **Leading Coefficient**: The leading coefficient is the coefficient of the leading term, which is **9**.

Summarizing:

- The expression represents a **polynomial** with **3 terms**.
- The constant term is **\(-6\)**, the leading term is **\(9x^5\)**, and the leading coefficient is **9**.