Solution Found!
Determine which of the polynomials below is (are)
Chapter 17, Problem 12E(choose chapter or problem)
QUESTION:
Determine which of the polynomials below is (are) irreducible over Q.
a. \(x^5 + 9x^4 + 12x^2 + 6 \)
b. \(x^4 + x + 1 \)
c. \(x^4 + 3x^2 + 3 \)
d. \(x^5 + 5x^2 + 1 \)
e. \((5/2)x^5 + (9/2)x^4 + 15x^3 + (3/7)x^2 + 6x + 3/14\)
Questions & Answers
QUESTION:
Determine which of the polynomials below is (are) irreducible over Q.
a. \(x^5 + 9x^4 + 12x^2 + 6 \)
b. \(x^4 + x + 1 \)
c. \(x^4 + 3x^2 + 3 \)
d. \(x^5 + 5x^2 + 1 \)
e. \((5/2)x^5 + (9/2)x^4 + 15x^3 + (3/7)x^2 + 6x + 3/14\)
ANSWER:Step 1 of 5
(a)
Eisenstein's criterion (Theorem 17.4) with implies that is irreducible over .