A polynomial and one of its factors is given. Factor the polynomial OMPLETELY given that one of its factors is x + 4. YOUR FINAL ANSWER SHOULD E IN FACTORED FORM! *
A polynomial and one of its factors is given. Factor the polynomial OMPLETELY given that one of its factors is x + 4. YOUR FINAL ANSWER SHOULD E IN FACTORED FORM! *
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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![### Polynomial Factorization and Finding Zeros
#### 3. Factor the Polynomial Completely
A polynomial and one of its factors is given. Factor the polynomial **completely** given that one of its factors is \(x + 4\).
**Given Polynomial:**
\[ f(x) = x^7 + 4x^6 + 7x^4 + 28x^3 - 8x - 32 \]
**Instructions:**
- Factor the polynomial completely.
- Your final answer should be in factored form.
Your answer: ______________________
**Note:** This is a required question.
---
#### 4. Find All Additional Real Zeros
Given that \( x = 6 \) is a zero of the polynomial, find all additional real zeros of the given polynomial.
**Given Polynomial:**
\[ f(x) = 4x^7 - 24x^6 - 25x^5 + 150x^4 - 4x^3 + 24x^2 + 25x - 150 \]
**Instructions:**
- Your final answer should be values of \( x \) that will make the equation true.
Your answer: ______________________
**Note:** This is a required question.
---
These exercises require in-depth understanding of polynomial factorization and finding zeros of polynomial equations. Make sure to apply the given factors and zeros accurately to achieve the correct solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3fd9fba-5a8f-483b-ab28-e1e51fab3fbe%2F71722c9d-b374-4b5e-a745-4c7b0e5db438%2Folkr0o_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Factorization and Finding Zeros
#### 3. Factor the Polynomial Completely
A polynomial and one of its factors is given. Factor the polynomial **completely** given that one of its factors is \(x + 4\).
**Given Polynomial:**
\[ f(x) = x^7 + 4x^6 + 7x^4 + 28x^3 - 8x - 32 \]
**Instructions:**
- Factor the polynomial completely.
- Your final answer should be in factored form.
Your answer: ______________________
**Note:** This is a required question.
---
#### 4. Find All Additional Real Zeros
Given that \( x = 6 \) is a zero of the polynomial, find all additional real zeros of the given polynomial.
**Given Polynomial:**
\[ f(x) = 4x^7 - 24x^6 - 25x^5 + 150x^4 - 4x^3 + 24x^2 + 25x - 150 \]
**Instructions:**
- Your final answer should be values of \( x \) that will make the equation true.
Your answer: ______________________
**Note:** This is a required question.
---
These exercises require in-depth understanding of polynomial factorization and finding zeros of polynomial equations. Make sure to apply the given factors and zeros accurately to achieve the correct solutions.
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