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Unformatted text preview: p 1 ( x ), . . . , p m ( x ) are monic irreducible polynomials, and q 1 ( x ), . . . , q n ( x ) are monic nonconstant polynomials, then q 1 ( x ), . . . , q n ( x ) are irreducible. Solution. False. (iv) If k is a f eld and f ( x ) k [ x ] can be written as ap 1 ( x ) p m ( x ) and bq 1 ( x ) q n ( x ) , where a , b are constants, p 1 ( x ), . . . , p m ( x ) are monic irreducible polynomials, and q 1 ( x ), . . . , q n ( x ) are monic nonconstant polynomials, then m n . Solution. True. (v) If k is a sub f eld of K and f ( x ) k [ x ] has the factorization f ( x ) = ap e 1 1 p e n n , where a is a constant and the p i ( x ) are monic irreducible in k [ x ] , then f ( x ) = ap e 1 1 p e n n is also the factorization of f ( x ) in K [ x ] as a product of a constant and monic irreducible polynomials. Solution. False....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
 Fall '11
 KeithCornell

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