Determine the coefficient of each​ term, the degree of each​ term, the degree of the​ polynomial, the leading​ term, and the leading coefficient of the following polynomial.

6 x Superscript 9 Baseline plus 9 x Superscript 6 Baseline minus 7 x Superscript 5 Baseline plus 76x9+9x6−7x5+7

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Part 1

The coefficient of the term 

6 x Superscript 96x9 

is 

enter your response here.

Part 2

The degree of the term 

6 x Superscript 96x9 

is 

enter your response here.

Part 3

The coefficient of the term 

9 x Superscript 69x6 

is 

enter your response here.

Part 4

The degree of the term 

9 x Superscript 69x6 

is 

enter your response here.

Part 5

The coefficient of the term 

negative 7 x Superscript 5−7x5 

is 

enter your response here.

Part 6

The degree of the term 

negative 7 x Superscript 5−7x5 

is 

enter your response here.

Part 7

The coefficient of the term 

77 

is 

enter your response here.

The degree of the term 

77 

is 

enter your response here.

Part 9

The degree of the polynomial 

6 x Superscript 9 Baseline plus 9 x Superscript 6 Baseline minus 7 x Superscript 5 Baseline plus 76x9+9x6−7x5+7 

is 

enter your response here.

Part 10

The leading term of the polynomial 

6 x Superscript 9 Baseline plus 9 x Superscript 6 Baseline minus 7 x Superscript 5 Baseline plus 76x9+9x6−7x5+7 

is 

enter your response here. 

Part 11

The leading coefficient of the polynomial 

6 x Superscript 9 Baseline plus 9 x Superscript 6 Baseline minus 7 x Superscript 5 Baseline plus 76x9+9x6−7x5+7 

is 

enter your response here.

Let's analyze the polynomial \( 6x^9 + 9x^6 - 7x^5 + 7 \) step by step.

### Part 1: Coefficient of \( 6x^9 \)
The coefficient of the term \( 6x^9 \) is \( 6 \).

### Part 2: Degree of \( 6x^9 \)
The degree of the term \( 6x^9 \) is \( 9 \).

### Part 3: Coefficient of \( 9x^6 \)
The coefficient of the term \( 9x^6 \) is \( 9 \).

### Part 4: Degree of \( 9x^6 \)
The degree of the term \( 9x^6 \) is \( 6 \).

### Part 5: Coefficient of \( -7x^5 \)
The coefficient of the term \( -7x^5 \) is \( -7 \).

### Part 6: Degree of \( -7x^5 \)
The degree of the term \( -7x^5 \) is \( 5 \).

### Part 7: Coefficient of \( 7 \)
The coefficient of the term \( 7 \) is \( 7 \).

### Part 8: Degree of \( 7 \)
The degree of the term \( 7 \) is \( 0 \). (Note: A constant term, like \( 7 \), has a degree of \( 0 \).)

### Part 9: Degree of the Polynomial
The degree of the polynomial \( 6x^9 + 9x^6 - 7x^5 + 7 \) is the highest degree of its terms, which is \( 9 \).

### Part 10: Leading Term of the Polynomial
The leading term of the polynomial \( 6x^9 + 9x^6 - 7x^5 + 7 \) is the term with the highest degree, which is \( 6x^9 \).

### Part 11: Leading Coefficient of the Polynomial
The leading coefficient of the polynomial \( 6x^9 + 9x^6 - 7x^5 + 7 \) is the coefficient of the leading term, which is \( 6 \).

Here is a summary of all parts:

1. **Coefficient of \( 6x^9 \)**: \( 6 \)
2. **Degree of \( 6x^9 \)**: \( 9 \)
3. **Coefficient of \( 9x^6 \)**: \( 9 \)
4. **Degree of \( 9x^6 \)**: \( 6 \)
5. **Coefficient of \( -7x^5 \)**: \( -7 \)
6. **Degree of \( -7x^5 \)**: \( 5 \)
7. **Coefficient of \( 7 \)**: \( 7 \)
8. **Degree of \( 7 \)**: \( 0 \)
9. **Degree of the Polynomial**: \( 9 \)
10. **Leading Term of the Polynomial**: \( 6x^9 \)
11. **Leading Coefficient of the Polynomial**: \( 6 \)

Would you like more details on any part, or do you have any further questions?

### Questions for further exploration:

1. What is the leading term of the polynomial \( 4x^8 + 2x^3 - 5x + 1 \)?
2. How do you find the degree of a polynomial with multiple variables?
3. What is the coefficient of \( x^2 \) in the polynomial \( 3x^4 + 5x^2 - 2x + 7 \)?
4. How does the leading coefficient affect the graph of a polynomial?
5. What is the degree of the polynomial \( x^3 + x^2 + x + 1 \)?
6. Can a polynomial have more than one leading term?
7. How do you find the degree of a polynomial with negative exponents?
8. What is the impact of a constant term on the overall degree of a polynomial?

### Tip:
When working with polynomials, always arrange the terms in descending order of their degrees. This helps in easily identifying the leading term and leading coefficient.

Explore the concepts of polynomials, coefficients, degrees, and leading terms with a detailed analysis of a given polynomial. Learn how to identify coefficients, degrees of terms, and determine the leading term and leading coefficient of a polynomial.

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