Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all real solutions of the equation. (Enter your answers as a comma-separated list.) x³2x²9x2=0, x=2-√5 X=
Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all real solutions of the equation. (Enter your answers as a comma-separated list.) x³2x²9x2=0, x=2-√5 X=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Title: Solving a Third-Degree Polynomial Using Synthetic Division**
**Instructions:**
Use synthetic division to show that \( x \) is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all real solutions of the equation. (Enter your answers as a comma-separated list.)
**Problem:**
Given the polynomial equation:
\[ x^3 - 2x^2 - 9x - 2 = 0 \]
with a suspected solution:
\[ x = 2 - \sqrt{5} \]
**Solution:**
\[ x = \boxed{} \]
Use synthetic division and the given solution to factor the polynomial and find all real solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2367e66-1ae4-4371-aa7b-db391deab840%2F0eff7e88-4236-4f99-92dc-6368bf8b505e%2Ffey504vr_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Solving a Third-Degree Polynomial Using Synthetic Division**
**Instructions:**
Use synthetic division to show that \( x \) is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all real solutions of the equation. (Enter your answers as a comma-separated list.)
**Problem:**
Given the polynomial equation:
\[ x^3 - 2x^2 - 9x - 2 = 0 \]
with a suspected solution:
\[ x = 2 - \sqrt{5} \]
**Solution:**
\[ x = \boxed{} \]
Use synthetic division and the given solution to factor the polynomial and find all real solutions.
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