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# question on irreducible polynomials watch

1. Hello there,
given that the field, F = 2/2Z (Z denotes the integers)

show that the polynomial x^2 + x + [1] is irreducible.

How do I do this??? A polynomial is irreducible if it factors into two polynomials, with one of them a constant polynomial. But how do I factor the given polynomia in this way?

ANy help would be much appreciated!!

2. Suppose it's reducible. This implies it's equal to:
(x - [b])(x - [d])

Can you see why that's impossible?
3. ahh yes,

cheers bud .

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Updated: April 13, 2006
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