MAD 4301 Midterm: MAS4301 F02 Test 2
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We say (i) f (x) is irreducible if . (ii) c is a root of f (x) if . (2) (15 pts. ) Give examples of the following, or state that none exists. No proofs required. (a) an irreducible polynomial of degree 3 in z2[x]. (b) an irreducible polynomial of degree 2 in z5[x]. (c) an irreducible polynomial of degree 3 in r[x]. (3) (15 pts. ) Let z = 1 + i c. for the following complex numbers nd the polar representations. That is, nd r and . (a) z (b) z2 (c) z (d) z (e) z 1 (5) (15 pts. ) Let f (x) = x3 + x2 2x 1 q[x]. Let c be a root of f (x). You may assume f (x) is irreducible in q[x]. Let f be a eld and f (x) a polynomial in f [x] of degree n 1.
