Let's analyze the given polynomial:
[tex]\[
-9s^3 + 2s^2 + 7s
\][/tex]
### Step 1: Identify and List the Terms
First, we need to recognize and list each term separately within the polynomial. The polynomial given is:
[tex]\[
-9s^3 + 2s^2 + 7s
\][/tex]
Here, the terms are:
1. [tex]\(-9s^3\)[/tex]
2. [tex]\(2s^2\)[/tex]
3. [tex]\(7s\)[/tex]
### Step 2: Count the Number of Terms
Next, we count the number of terms we have listed. From the list, we can see:
1. [tex]\(-9s^3\)[/tex]
2. [tex]\(2s^2\)[/tex]
3. [tex]\(7s\)[/tex]
Thus, the polynomial consists of 3 distinct terms.
### Step 3: Determine the Degree of Each Term
The degree of a term in a polynomial is the exponent of the variable in that term.
- For the term [tex]\(-9s^3\)[/tex], the degree is [tex]\(3\)[/tex] because the exponent of [tex]\(s\)[/tex] is [tex]\(3\)[/tex].
- For the term [tex]\(2s^2\)[/tex], the degree is [tex]\(2\)[/tex] because the exponent of [tex]\(s\)[/tex] is [tex]\(2\)[/tex].
- For the term [tex]\(7s\)[/tex], the degree is [tex]\(1\)[/tex] because the exponent of [tex]\(s\)[/tex] is [tex]\(1\)[/tex].
### Step 4: Find the Degree of the Polynomial
The degree of the polynomial is the highest degree of any term within it. Looking at the degrees we identified:
[tex]\[
\begin{align*}
-9s^3 &\quad \text{has degree} \, 3 \\
2s^2 &\quad \text{has degree} \, 2 \\
7s &\quad \text{has degree} \, 1
\end{align*}
\][/tex]
The highest degree among these is [tex]\(3\)[/tex].
### Conclusion
Therefore, the polynomial [tex]\(-9s^3 + 2s^2 + 7s\)[/tex] has:
- Number of terms: 3
- Degree of the polynomial: 3
In summary, the number of terms in the polynomial is 3, and the degree of the polynomial is 3.
