For each $f \in K[x]$, find a monic polynomial satisfied by $f$ with coefficients in $K[x^2]$, where $K$ is a field.
2026-03-25 06:09:02.1774418942
Find a monic polynomial
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Hint: Try $$ (T-f(x))(T-f(-x)). $$ The coefficients of various powers of $T$ are in $K[x^2]$, iff they are even polynomials.