Homework Soursed Find the irreducible factorization of X4 2 in KX Let I F3
(d) Find the irreducible factorization of X^4 + 2 in K[X].
Let I F3 {x} be the ideal generated by X62 + 1, that is I = (x^2 +1 ) (a) Show that X^4 + 2 is in I. (b) Show that K = F3[X]/I is a field. (c) Find the irreducible factorization of X^4 + 2 in F3[X]. (d) Find the irreducible factorization of X^4 + 2 in K[X].Solution
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![(d) Find the irreducible factorization of X^4 + 2 in K[X]. Let I F3 {x} be the ideal generated by X62 + 1, that is I = (x^2 +1 ) (a) Show that X^4 + 2 is in I.](/WebImages/10/d-find-the-irreducible-factorization-of-x4-2-in-kx-let-i-f3-1004030-1761517417-0.webp "(d) Find the irreducible factorization of X^4 + 2 in K[X]. Let I F3 {x} be the ideal generated by X62 + 1, that is I = (x^2 +1 ) (a) Show that X^4 + 2 is in I.")
