Show that the set of polynomials in Q[x] that vanish on {1,2,3} is an ideal in Q[x]...
Not sure how to begin this one. What does it mean {1,2,3} vanishes?
2026-04-07 06:14:28.1775542468
Set of Polynomials in Q[x] vanish on {1,2,3} is an ideal in Q[x]
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You need to show that the set of polynomials $p \in \mathbb Q[x]$ such that $p(1) = p(2) = p(3) = 0$ is stable by sum, and by product (i.e if $p$ is such a polynomial and $q$ an arbitrary polynomial then $pq$ is a polynomial which vanishes at $\{1,2,3\}$).