Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Finding Complex Zeros of a Polynomial Function
**Problem Statement:**
Find the complex zeros of the following polynomial function and write \( f \) in factored form.
\[ f(x) = x^4 + 4x^3 + 4x^2 + 36x - 45 \]
---
**Steps:**
1. **Finding the Complex Zeros:**
To find the complex zeros of \( f(x) \), we need to solve the equation:
\[ x^4 + 4x^3 + 4x^2 + 36x - 45 = 0 \]
(Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
**Answer Box:**
\[ \text{The complex zeros of } f \text{ are } \_\_\_\_\_\_. \]
---
2. **Factoring the Polynomial:**
Next, use the complex zeros to factor \( f \).
**Answer Box:**
\[ f(x) = \_\_\_\_\_\_ \]
(Type your answer in factored form. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression.)
---
**Final Instruction:**
Enter your answer in each of the answer boxes provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6811bcd-02f8-46fa-b044-8f44b9c4930d%2Fd555ce29-06c6-4a4e-afb0-e88af7da93a6%2F3pxhnam.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding Complex Zeros of a Polynomial Function
**Problem Statement:**
Find the complex zeros of the following polynomial function and write \( f \) in factored form.
\[ f(x) = x^4 + 4x^3 + 4x^2 + 36x - 45 \]
---
**Steps:**
1. **Finding the Complex Zeros:**
To find the complex zeros of \( f(x) \), we need to solve the equation:
\[ x^4 + 4x^3 + 4x^2 + 36x - 45 = 0 \]
(Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
**Answer Box:**
\[ \text{The complex zeros of } f \text{ are } \_\_\_\_\_\_. \]
---
2. **Factoring the Polynomial:**
Next, use the complex zeros to factor \( f \).
**Answer Box:**
\[ f(x) = \_\_\_\_\_\_ \]
(Type your answer in factored form. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression.)
---
**Final Instruction:**
Enter your answer in each of the answer boxes provided.
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