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.

x cubed plus x squaredx3+x2

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Part 1

The coefficient of the term 

x cubedx3 

is 

enter your response here.

Part 2

The degree of the term 

x cubedx3 

is 

enter your response here.

Part 3

The coefficient of the term 

x squaredx2 

is 

enter your response here.

Part 4

The degree of the term 

x squaredx2 

is 

enter your response here.

Part 5

The degree of the polynomial is 

enter your response here.

Part 6

The leading term of the polynomial is 

enter your response here.
 
Part 7

The leading coefficient of the polynomial is 

enter your response here.

Let's break down the polynomial \( x^3 + x^2 \) and determine the required information.

### Part 1: Coefficient of \( x^3 \)
The coefficient of the term \( x^3 \) is \( 1 \), since \( x^3 \) is equivalent to \( 1 \cdot x^3 \).

### Part 2: Degree of \( x^3 \)
The degree of the term \( x^3 \) is \( 3 \), which is the exponent of \( x \).

### Part 3: Coefficient of \( x^2 \)
The coefficient of the term \( x^2 \) is \( 1 \), since \( x^2 \) is equivalent to \( 1 \cdot x^2 \).

### Part 4: Degree of \( x^2 \)
The degree of the term \( x^2 \) is \( 2 \), which is the exponent of \( x \).

### Part 5: Degree of the Polynomial
The degree of the polynomial \( x^3 + x^2 \) is the highest degree of its terms, which is \( 3 \).

### Part 6: Leading Term of the Polynomial
The leading term of the polynomial \( x^3 + x^2 \) is the term with the highest degree, which is \( x^3 \).

### Part 7: Leading Coefficient of the Polynomial
The leading coefficient of the polynomial \( x^3 + x^2 \) is the coefficient of the leading term, which is \( 1 \).

Here is a summary of all parts:

1. **Coefficient of \( x^3 \)**: \( 1 \)
2. **Degree of \( x^3 \)**: \( 3 \)
3. **Coefficient of \( x^2 \)**: \( 1 \)
4. **Degree of \( x^2 \)**: \( 2 \)
5. **Degree of the Polynomial**: \( 3 \)
6. **Leading Term of the Polynomial**: \( x^3 \)
7. **Leading Coefficient of the Polynomial**: \( 1 \)

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

### Questions for further exploration:

1. What is the coefficient of \( x \) in the polynomial \( 2x^3 + 4x^2 + 3x + 5 \)?
2. How do you determine the degree of a polynomial with multiple terms?
3. What is the leading term of the polynomial \( -7x^5 + 3x^3 - x + 9 \)?
4. What is the degree of the polynomial \( x^4 + 2x^3 + x^2 + x + 1 \)?
5. How do you find the coefficient of a specific term in a polynomial?
6. What is the leading coefficient of the polynomial \( 5x^3 - 2x^2 + x - 8 \)?
7. How does the degree of a polynomial affect its graph?
8. What is the general form of a polynomial of degree \( n \)?

### Tip:
When determining the degree of a polynomial, always look for the term with the highest exponent. This highest exponent indicates the degree of the polynomial.

Explore the polynomial x^3 + x^2 and understand its coefficients, degrees of terms, degree of the polynomial, leading term, and leading coefficient. Learn key concepts in polynomial algebra suitable for Grades 7-9.

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