Given and an image polynomials b(x) = 48x422³ +47x²+144 uo(x) = x² + 4x+2 and wo=2²+4x+5 satisfying b = 6uo wo (mod 7), lift the image polynomials using Hensel lifting to find (if there exist) u and w in Z[r] such that b = uw.

Q: Let G=Z5xZ6X Z9 X Z12- Find the elementary divisors and invariant factors of G.

A: Solution :-

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A: We know that results

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A: Please see the next step for solution

Q: Let f(x) = x² +1 € Z3[x] and let R= Z3[x]/I, where I = (f(x)). (a) Show that R is a field with 9…

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A: Solution :-

Q: 2d

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A: Polynomial a is reducible.