Unformatted text preview: Q [ x ] / ( p ( x )). 6. Let F = Z 2 and let f ( x ) = x 3 + x +1 ∈ F [ x ]. Suppose a is a zero of f ( x ) in some extension of F . How many elements does F ( a ) have? Express each member of F ( a ) in terms of a . Write out a complete multiplication table for F ( a )....
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 Spring '11
 Johnson
 Algebra, Complex number, splitting field, complete multiplication table

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