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.

9 x Superscript 7 Baseline plus 2 x squared minus 3 x plus 69x7+2x2−3x+6

Question content area bottom

Part 1

The coefficient of the term 

9 x Superscript 79x7 

is 

enter your response here.

To analyze the polynomial \( 9x^7 + 2x^2 - 3x + 6 \), let's identify each component systematically.

1. **Coefficient of each term:**
   - For \( 9x^7 \), the coefficient is **9**.
   - For \( 2x^2 \), the coefficient is **2**.
   - For \( -3x \), the coefficient is **-3**.
   - For the constant term \( 6 \), the coefficient is **6**.

2. **Degree of each term:**
   - The term \( 9x^7 \) has a degree of **7**.
   - The term \( 2x^2 \) has a degree of **2**.
   - The term \( -3x \) has a degree of **1**.
   - The constant term \( 6 \) has a degree of **0**.

3. **Degree of the polynomial:** The highest degree of the terms in the polynomial is **7**.

4. **Leading term:** The leading term, which has the highest degree, is \( 9x^7 \).

5. **Leading coefficient:** The coefficient of the leading term is **9**.

---

**Answer for Part 1:**
The coefficient of the term \( 9x^7 \) is **9**.

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

Here are some related questions to explore further:
1. How does the sign of the leading coefficient affect the graph of a polynomial?
2. What is the role of the constant term in a polynomial?
3. How can you determine if a polynomial is even or odd?
4. What methods can be used to factor a polynomial?
5. How can the degree of a polynomial affect the number of roots it has?
6. What are the possible end behaviors of a polynomial function?
7. How do you determine the multiplicity of a root in a polynomial?
8. Can a polynomial have a fractional exponent?

**Tip:** When identifying coefficients, remember that each term's coefficient is the number directly in front of the variable or variable expression, including any sign (positive or negative).

Understand how to identify coefficients and degrees in polynomials using an example problem. Learn about polynomial terms, their degrees, leading terms, and leading coefficients. Suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation