Is $\{p(x) ∈ \Bbb Q[x] \mid p(0) = 3\}$ an ideal of $\Bbb Q[x]$?

I don't have any idea of how to start this problem. Any help would be great, thank you in advance!


closed as off-topic by user21820, Lee David Chung Lin, Cornman, Cesareo, heropup May 6 at 1:02

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  • 4
    $\begingroup$ "I don't have any idea how to start..." First thing to do: Write down the definition of "ideal". $\endgroup$ – GEdgar Apr 21 at 21:46
  • $\begingroup$ Here's a MathJax tutorial :) $\endgroup$ – Shaun Apr 21 at 21:47
  • 1
    $\begingroup$ Is this set stable by addition? By scalar multiplication? $\endgroup$ – Bernard Apr 21 at 21:50
  • $\begingroup$ Is $0$ in the ideal? Remember, any ideal of $\Bbb{Q}[x]$ must also be a subgroup under addition of $\Bbb{Q}[x]$. $\endgroup$ – Chickenmancer Apr 21 at 21:55

Ideals got to be closed under addition. But for $f,g\in$ your set, $$ (f+g)(0)=f(0)+g(0)=3+3=6\neq3, $$ so $f+g\notin$ your set. You set is not an ideal.


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