Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. s(x) = x + 4x – 64x – 256 ; x + 4 s(x) = D
Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. s(x) = x + 4x – 64x – 256 ; x + 4 s(x) = D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![**Educational Exercise: Polynomial Factorization**
**Objective:** Show that the given binomial is a factor of the polynomial, then factor the polynomial completely.
**Problem Statement:**
Given the polynomial:
\[ s(x) = x^4 + 4x^3 - 64x - 256 \]
and the binomial:
\[ x + 4 \]
**Tasks:**
1. Demonstrate that \( x + 4 \) is a factor of \( s(x) \).
2. Factor the polynomial \( s(x) \) completely.
**Solution Approach:**
Start by using polynomial division or the Remainder Theorem to verify if \( x + 4 \) is a factor. If the remainder is zero, then \( x + 4 \) is a factor.
Proceed to factorize the polynomial completely by further breaking down the quotient obtained from the division process.
**Further Explanation:**
Explain each step of the division and factorization in detail, providing insights into methods used, such as synthetic division or long division for polynomials.
Conclude with a fully factored expression of \( s(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67f5cb0-daee-4ea8-9bfc-4a00f267029a%2F89db075f-41e8-4e6d-80ba-68143437c8db%2Fnhxm5cc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Exercise: Polynomial Factorization**
**Objective:** Show that the given binomial is a factor of the polynomial, then factor the polynomial completely.
**Problem Statement:**
Given the polynomial:
\[ s(x) = x^4 + 4x^3 - 64x - 256 \]
and the binomial:
\[ x + 4 \]
**Tasks:**
1. Demonstrate that \( x + 4 \) is a factor of \( s(x) \).
2. Factor the polynomial \( s(x) \) completely.
**Solution Approach:**
Start by using polynomial division or the Remainder Theorem to verify if \( x + 4 \) is a factor. If the remainder is zero, then \( x + 4 \) is a factor.
Proceed to factorize the polynomial completely by further breaking down the quotient obtained from the division process.
**Further Explanation:**
Explain each step of the division and factorization in detail, providing insights into methods used, such as synthetic division or long division for polynomials.
Conclude with a fully factored expression of \( s(x) \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
