# 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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### What is the probability of interpolating the Tutte polynomial of a planar graph from the values at the two hyperbolas?

Crossposted from MO The Tutte polynomial is a bivariate polynomial with positive integer coefficient which is a graph invariant and can be defined recursively. Evaluating it is $\#P$-complete even ...
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### Checking whether a given polynomial is reducible or irreducible.

We're given the polynomial $x^{2}-2$ , and we need to prove that it's irreducible in $\mathbb Q$ but reducible in $\mathbb R$. Writing the polynomial as $(x^{2}-2) = 1.(x^{2}-2)$ , $(x^{2}-2)$ ...
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### Solving a polynomial for cyclic roots

For any complex value of c, the following polynomial has 6 complex root values of p: $$1+c+2 c^2+c^3+p+2 c p+c^2 p+p^2+3 c p^2+3 c^2 p^2+p^3+2 c p^3+p^4+3 c p^4+p^5+p^6$$ For a general 6th order ...
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### A subset of easily solved quartic polynomials

I've found (maybe, maybe not, but it's not on this Wikipedia or this Wikipedia) that there is a subset of easily solved quartic polynomials of the form ...
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### Closed form for the sole positive root of the polynomial ${x^\alpha } + {x^{\alpha - 1}} + \cdots + {x^3} + {x^2} -p$, $p > 0$

For a study I'm making about the minimum and maximum radial values of bounded orbits in a central force system with general power law forces, I came across this special polynomial equation: ...
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### Determining if a Polynomial is a subspace and its Basis

Hi, the question is Which of the subsets of P2 given in Exercises 1 through 5 are subspaces of P2 Find a basis for those that are subspaces. So I know that P'(1) = 1b + 2c And I know that P(2) = a ...
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### Polynomial Factoring problem [on hold]

Find the value of $p$ and $q$ such that $15x^3 + 26x^2 - 11x - 6$ is a factor of $15x^4 + px^3 - 37x^2 + qx + 6$.
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### Finding a sixth degree polynomial that goes through 8 points

For a summative math research assignment, I will have to find a sixth degree polynomial that would ideally go through the following points: (0, 20.5625) (10, 27.5625) (30, 14.5625) (50, 14.6875) (60, ...
### How to prove if $5/2 < x < (5/4)(1+\sqrt2)$, then $25/(x(2x-5)\ge 8$
if $\frac52 < x < \frac54(1+\sqrt2)$, then $\frac{25}{x(2x-5)} \ge 8$ First I unpacked the conclusion to: $$16w^2-40w-25 \le 0$$ I attempted to solve by manipulating the interval (squaring, ...