# Tagged Questions

This tag is used for both basic and advanced questions on polynomials in any number of variables. Including, but not limited to: solving for roots, factoring, checking for irreducibility. This tag is rarely used as the only tag for a question.

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### Factorisation of a polynomial

How to factorize $a^6+8a^3+27$, I got different answers but one of the answers is $(a^2-a+3)(a^4+a^3-2a^2+3a+9)$, can someone tell me how to get this answer? Thanks
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### Construction of a 8-degree polynomial with 16 real numbers

(Vietnam TST 2016/6) Given $16$ distinct real numbers $\alpha_1,\alpha_2,\ldots,\alpha_{16}$. For each polynomial $P$, denote $$V(P)=P(\alpha_1)+P(\alpha_2)+\cdots+P(\alpha_{16}).$$Prove that there ...
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### Two questions on the Gaussian integers [duplicate]

I have two questions on the Gaussian integers. Is any element in $\mathbb{Z}[i]$ the root of a monic polynomial with coefficients in $\mathbb{Z}$? Conversely, does any element in $\mathbb{Q}(i)$ ...
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### On the maximal of polynomial at a point

I faced this problem when I studied polynomial. Let $p(x)=ax^3+bx^2+cx+d$ be a cubic polynomial with real coefficients, and $p(5)+p(25)=1906$. Find the maximal value of $|p(15)|$. I ...
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### relationship between independence of multivariate polynomials, generating sets of polynomial ideals

I am studying something that touches on Groebner algorithms at the moment and It seems like i am missing something obvious about the relationship between three definitions that feel like they should ...
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