# 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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### How to find area of a polygon built on the roots of a given polynomial?

How to find the area of a (maximum area convex) polygon, built on the roots of a given polynomial in the complex plane? For example, consider the equation: $$2x^5+3x^3-x+1=0$$ It has one real and ...
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### Number of irreducible polynomial over a field. [closed]

Find the number of irreducible monic polynomials of degree $2$ over a field with five elements. Please anyone help me.
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### How does Gauss's lemma follow from Nagata's lemma?

In section 4 of Samuel's Unique Factorization it's said Gauss' lemma is an easy consequence of Nagata's lemma. How does this work, i.e., how to deduce Gauss' lemma from Nagata's lemma? I'm asking ...
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### Solve $\int{\sqrt{1 + (3x^2 + 2x - \frac{29}{2})^2}} dx$
I have to solve this indefine integral: $$\int{\sqrt{1 + (3x^2 + 2x - \frac{29}{2})^2}} dx$$ I tried to make the square: $$\int{\sqrt{9x^4 +12x^3-29*3x^2 -58x + \frac{29^2 +4}{4}}} dx$$ but ...