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Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

Advanced Engineering Mathematics
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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Test the polynomial x4 – 2x³ + 6x – 3 for irreducibility over Q.
Transcribed Image Text:Test the polynomial x4 – 2x³ + 6x – 3 for irreducibility over Q.
Expert Solution
Step 1

We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of

rational numbers ℚ or not.

Let px=a4x4+a3x3+a2x2+a1x+a0 where a0=-3, a1=6, a2=0, a3=-2 and

a4=1. We will use the irreducibility criteria.

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