Give the degree and leading coefficient of the following polynomial function. f(z) = g5 (5 – 5g3 – 1z3 x5 52³ 47³) Degree: Number Leading Coefficient: Number
Give the degree and leading coefficient of the following polynomial function. f(z) = g5 (5 – 5g3 – 1z3 x5 52³ 47³) Degree: Number Leading Coefficient: Number
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
![**Polynomial Function Analysis**
**Problem Statement:**
Give the degree and leading coefficient of the following polynomial function.
\[ f(x) = x^5 \left(5 - 5x^3 - 4x^3 \right) \]
**Instructions:**
1. Identify the degree of the polynomial.
2. Determine the leading coefficient.
**Degree:**
\[ \boxed{\text{Number}} \]
**Leading Coefficient:**
\[ \boxed{\text{Number}} \]
---
**Explanation:**
To find the degree and leading coefficient of the polynomial function \( f(x) \), we first need to simplify the function inside the parentheses and then multiply by \( x^5 \).
Let's simplify step by step.
1. Inside the parentheses:
\[ 5 - 5x^3 - 4x^3 = 5 - 9x^3 \]
2. Now, the function becomes:
\[ f(x) = x^5 (5 - 9x^3) \]
3. Distribute \( x^5 \):
\[ f(x) = 5x^5 - 9x^8 \]
Now that we have the polynomial in standard form \( f(x) = 5x^5 - 9x^8 \), we can determine the degree and the leading coefficient.
4. The degree of the polynomial is the highest power of \( x \) in the polynomial:
\[ \text{Degree} = 8 \]
5. The leading coefficient is the coefficient of the term with the highest power of \( x \):
\[ \text{Leading Coefficient} = -9 \]
So, the answers are:
- Degree:
\[ \boxed{8} \]
- Leading Coefficient:
\[ \boxed{-9} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0cced35-ae0d-464b-8bca-6dbaa684602c%2F68c044c9-6d4d-46b8-b54e-a6eee1c63f19%2Fqdze24a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Polynomial Function Analysis**
**Problem Statement:**
Give the degree and leading coefficient of the following polynomial function.
\[ f(x) = x^5 \left(5 - 5x^3 - 4x^3 \right) \]
**Instructions:**
1. Identify the degree of the polynomial.
2. Determine the leading coefficient.
**Degree:**
\[ \boxed{\text{Number}} \]
**Leading Coefficient:**
\[ \boxed{\text{Number}} \]
---
**Explanation:**
To find the degree and leading coefficient of the polynomial function \( f(x) \), we first need to simplify the function inside the parentheses and then multiply by \( x^5 \).
Let's simplify step by step.
1. Inside the parentheses:
\[ 5 - 5x^3 - 4x^3 = 5 - 9x^3 \]
2. Now, the function becomes:
\[ f(x) = x^5 (5 - 9x^3) \]
3. Distribute \( x^5 \):
\[ f(x) = 5x^5 - 9x^8 \]
Now that we have the polynomial in standard form \( f(x) = 5x^5 - 9x^8 \), we can determine the degree and the leading coefficient.
4. The degree of the polynomial is the highest power of \( x \) in the polynomial:
\[ \text{Degree} = 8 \]
5. The leading coefficient is the coefficient of the term with the highest power of \( x \):
\[ \text{Leading Coefficient} = -9 \]
So, the answers are:
- Degree:
\[ \boxed{8} \]
- Leading Coefficient:
\[ \boxed{-9} \]
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