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 Superscript 8 Baseline minus x cubed
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Part 1
The coefficient of the term x Superscript 8 is

enter your response here.

Let's analyze the polynomial \( x^8 - x^3 \).

1. **Coefficient of each term:**
   - For \( x^8 \), the coefficient is **1**.
   - For \( -x^3 \), the coefficient is **-1**.

2. **Degree of each term:**
   - The term \( x^8 \) has a degree of **8**.
   - The term \( -x^3 \) has a degree of **3**.

3. **Degree of the polynomial:** The degree of a polynomial is the highest degree of its terms. Therefore, the degree of the polynomial is **8**.

4. **Leading term:** The leading term is the term with the highest degree, which is \( x^8 \).

5. **Leading coefficient:** The coefficient of the leading term is **1**.

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**Answer for Part 1:**
The coefficient of the term \( x^8 \) is **1**.

Would you like details on any part of this explanation, or do you have any other questions?

Here are some related questions you might consider:
1. What is the constant term in a polynomial?
2. How do you find the degree of a polynomial function?
3. What is the importance of the leading coefficient in determining the end behavior of a polynomial?
4. How do you identify the leading term in a polynomial expression?
5. Can the degree of a polynomial be negative?
6. How do you determine if a polynomial is a monomial, binomial, or trinomial?
7. What is the difference between a term and a factor in a polynomial?
8. How do you factorize a polynomial?

**Tip:** When identifying the leading term and coefficient, always arrange the polynomial in descending order of degree.

Understand the coefficients and degrees of terms in the polynomial x^8 - x^3. Learn how to identify the leading term and coefficient, and determine the degree of the polynomial. Suitable for high school students.

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