Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Finding the Degree and Leading Coefficient of a Polynomial**
To determine the degree and leading coefficient of the given polynomial, follow these steps.
**Polynomial:**
\[ -2x^2 - 8x^4 + x - 7 \]
**Steps:**
1. **Find the Degree:**
The degree of a polynomial is the highest power of the variable \( x \). In this polynomial, the term with the highest power of \( x \) is \( -8x^4 \). Therefore, the degree of the polynomial is 4.
2. **Identify the Leading Coefficient:**
The leading coefficient is the coefficient of the term with the highest power of \( x \). For the term \( -8x^4 \), the coefficient is \( -8 \). Therefore, the leading coefficient is \(-8\).
**Conclusion:**
- Degree of the polynomial: **4**
- Leading coefficient: **-8**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85f8d668-e001-4163-8026-761ad4adc62e%2F3fa93529-68a2-49e1-8345-f481fdeb5941%2Fpwzkk6c_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Degree and Leading Coefficient of a Polynomial**
To determine the degree and leading coefficient of the given polynomial, follow these steps.
**Polynomial:**
\[ -2x^2 - 8x^4 + x - 7 \]
**Steps:**
1. **Find the Degree:**
The degree of a polynomial is the highest power of the variable \( x \). In this polynomial, the term with the highest power of \( x \) is \( -8x^4 \). Therefore, the degree of the polynomial is 4.
2. **Identify the Leading Coefficient:**
The leading coefficient is the coefficient of the term with the highest power of \( x \). For the term \( -8x^4 \), the coefficient is \( -8 \). Therefore, the leading coefficient is \(-8\).
**Conclusion:**
- Degree of the polynomial: **4**
- Leading coefficient: **-8**
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