Find a linear polynomial $A(x) ∈ (\Bbb Z/5\Bbb Z)[x]$ such that $$\bar A(x) = 2x^4 + x^3 + 2x + 1 \in (\Bbb Z/5\Bbb Z)[x]/(x^2 + x + 2)$$
2026-03-28 08:49:05.1774687745
Finding polynomials in Quotient rings with ideals
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Hint: In $(\Bbb Z/5\Bbb Z)[x]/(x^2 + x + 2)$, we have $x^2 = -x-2$. Use that to find other polynomials, of lower degree, that are congruent to $\bar A(x)$.