Introduction to Question 2

[tex]3x^9 + 7x^7 - 3x^3 + 2[/tex]

1. The degree of the term [tex]3x^9[/tex] is 9.
2. The coefficient of the term [tex]7x^7[/tex] is 7.
3. The degree of the term [tex]7x^7[/tex] is 7.
4. The coefficient of the term [tex]-3x^3[/tex] is -3.
5. The degree of the term [tex]-3x^3[/tex] is 3.
6. The coefficient of the term 2 is 2.
7. The degree of the term 2 is 0.
8. The degree of the polynomial [tex]3x^9 + 7x^7 - 3x^3 + 2[/tex] is 9.
9. The leading term of the polynomial [tex]3x^9 + 7x^7 - 3x^3 + 2[/tex] is [tex]3x^9[/tex].

Certainly! Let's break this down step-by-step.

The polynomial given is:

[tex]\[ 3x^9 + 7x^7 - 3x^3 + 2 \][/tex]

### 1. Identifying the Coefficients and Degrees of Each Term

- Term: [tex]$ 3x^9 $[/tex]
- Coefficient: 3
- Degree: 9

- Term: [tex]$ 7x^7 $[/tex]
- Coefficient: 7
- Degree: 7

- Term: [tex]$ -3x^3 $[/tex]
- Coefficient: -3
- Degree: 3

- Term: [tex]$ 2 $[/tex]
- Coefficient: 2
- Degree: 0

### 2. Summarizing the Coefficients and Degrees

Let's summarize the information we gathered.

- Coeficient of [tex]$ 3x^9 $[/tex]: 3
- Degree of [tex]$ 3x^9 $[/tex]: 9

- Coefficient of [tex]$ 7x^7 $[/tex]: 7
- Degree of [tex]$ 7x^7 $[/tex]: 7

- Coefficient of [tex]$ -3x^3 $[/tex]: -3
- Degree of [tex]$ -3x^3 $[/tex]: 3

- Coefficient of [tex]$ 2 $[/tex]: 2
- Degree of [tex]$ 2 $[/tex]: 0

### 3. Determining the Degree of the Polynomial

The degree of a polynomial is the highest degree of its terms. The degrees of the terms in this polynomial are 9, 7, 3, and 0. Therefore, the highest degree is:

[tex]\[ \text{Degree of the polynomial} = 9 \][/tex]

### 4. Finding the Leading Term

The leading term of a polynomial is the term with the highest degree. Here, the term with the highest degree (9) is [tex]$ 3x^9 $[/tex].

Therefore, the leading term of the polynomial is:

[tex]\[ 3x^9 \][/tex]

### Summary:

- The coefficient of the term [tex]$ 3x^9 $[/tex] is 3.
- The degree of the term [tex]$ 3x^9 $[/tex] is 9.
- The coefficient of the term [tex]$ 7x^7 $[/tex] is 7.
- The degree of the term [tex]$ 7x^7 $[/tex] is 7.
- The coefficient of the term [tex]$ -3x^3 $[/tex] is -3.
- The degree of the term [tex]$ -3x^3 $[/tex] is 3.
- The coefficient of the term [tex]$ 2 $[/tex] is 2.
- The degree of the term [tex]$ 2 $[/tex] is 0.
- The degree of the polynomial [tex]$ 3x^9 + 7x^7 - 3x^3 + 2 $[/tex] is 9.
- The leading term of the polynomial [tex]$ 3x^9 + 7x^7 - 3x^3 + 2 $[/tex] is 3x^9.

This concludes the detailed breakdown of the problem! If you have any more questions or need further clarification, feel free to ask!