# Factoring Quartic Polynomials: A Lost Art

@article{Brookfield2007FactoringQP, title={Factoring Quartic Polynomials: A Lost Art}, author={Gary Brookfield}, journal={Mathematics Magazine}, year={2007}, volume={80}, pages={67 - 70} }

(2007). Factoring Quartic Polynomials: A Lost Art. Mathematics Magazine: Vol. 80, No. 1, pp. 67-70.

## 17 Citations

### Remainder and quotient without polynomial long division

- Mathematics
- 2020

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the…

### In nite families of reciprocal monogenic polynomials and their Galois groups

- Mathematics
- 2021

We prove a new irreducibility theorem for a particular class of polynomials, and we use it to construct in nite families of reciprocal monogenic polynomials. These results extend previous work on…

### An Interesting Construction Problem

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A collection of simple construction problems is presented and conditions for which the construction can be carried out with compass and straightedge are determined.

### Galois Groups of Certain Even Octic Polynomials

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. Let f ( x ) = x 8 + ax 4 + b ∈ Q [ x ] be an irreducible polynomial where b is a square. We give a method that completely describes the factorization patterns of a linear resolvent of f ( x ) using…

### Quadratic Residues and the Frobenius Coin Problem

- Mathematics
- 2007

1. G. D. Birkhoff, A set of postulates for plane geometry based on scale and protractor, Ann. Math., 33 (1932) 329-345. 2. B. Bold, Famous Problems of Geometry and How To Solve Them, Dover, 1969. 3.…

### Galois groups of chromatic polynomials

- Mathematics
- 2012

The chromatic polynomial P ( G, λ ) gives the number of ways a graph G can be properly coloured in at most λ colours. This polynomial has been extensively studied in both combinatorics and…

### J an 2 02 2 The solutions to single-variable polynomials , implemented and verified in Lean An experience report on learning how to use a computer proof assistant

- Computer Science, Mathematics
- 2022

This work describes the learning experience of a starting Lean user, including a detailed comparison between the authors' work in Lean and very closely related work in Coq, and describes the solutions of quadratic, cubic, and quartic polynomials over certain fields.

### Two Families of Monogenic $S_4$ Quartic Number Fields

- Mathematics
- 2018

Consider the integral polynomials $f_{a,b}(x)=x^4+ax+b$ and $g_{c,d}(x)=x^4+cx^3+d$. Suppose $f_{a,b}(x)$ and $g_{c,d}(x)$ are irreducible, $b\mid a$, and the integers $b$, $d$, $256d-27c^4$, and…

### Regularization of the boundary integrals in the bem analysis of 3D potential problems

- Mathematics
- 2013

In the conventional boundary element analysis, near-singularities are present in the associated boundary integral equation for problems involving ultra-thin media. For this case, any conventional…

### The true maximum-likelihood estimators for the generalized Gaussian distribution with p = 3, 4, 5

- Mathematics
- 2017

ABSTRACT The generalized Gaussian distribution with location parameter μ, scale parameter σ, and shape parameter p contains the Laplace, normal, and uniform distributions as particular cases for p =…

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