Polynomial of Least Degree

Question

What is polynomial of the least degree? How is it different from a polynomial of any degree? Is it possible to give some examples? I came across this from the definition of minimal polynomial of a in a field.

Thanks

$x^4-4$ is a polynomial having root $\sqrt2$, but $x^2-2$ is a polynomial of least degree having root $\sqrt2$ — J. W. Tanner, Mar 06 '20 at 01:16
I meant a polynomial in $\mathbb Q[x]$; otherwise $x-\sqrt2$ would be a polynomial of least degree — J. W. Tanner, Mar 06 '20 at 01:30

score 1 · Accepted Answer · answered Mar 06 '20 at 01:27

1

It means a polynomial of degree $d$ having whatever property is being discussed, where there do not exist polynomials having that property and degree less than $d$.

answered Mar 06 '20 at 01:27

Robert Israel

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Polynomial of Least Degree

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