# The factorization of $f\left(x\right){x}^{n}+g\left(x\right)$ with $f\left(x\right)$ monic and of degree $\le 2$.

Joshua Harrington^{[1]}; Andrew Vincent^{[2]}; Daniel White^{[1]}

- [1] Department of Mathematics University of South Carolina Columbia, SC 29208
- [2] Department of Mathematics University of South Carolina Columbia, SC, 29208

Journal de Théorie des Nombres de Bordeaux (2013)

- Volume: 25, Issue: 3, page 565-578
- ISSN: 1246-7405

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topHarrington, Joshua, Vincent, Andrew, and White, Daniel. "The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.." Journal de Théorie des Nombres de Bordeaux 25.3 (2013): 565-578. <http://eudml.org/doc/275722>.

@article{Harrington2013,

abstract = {In this paper we investigate the factorization of the polynomials $f(x)x^n+g(x)\in \mathbb\{Z\}[x]$ in the special case where $f(x)$ is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that $f(x)$ is monic and linear.},

affiliation = {Department of Mathematics University of South Carolina Columbia, SC 29208; Department of Mathematics University of South Carolina Columbia, SC, 29208; Department of Mathematics University of South Carolina Columbia, SC 29208},

author = {Harrington, Joshua, Vincent, Andrew, White, Daniel},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {polynomials; trinomials; irreducible; factorization; irreducibility criteria; factorization of polynomials; quadratic polynomial},

language = {eng},

month = {11},

number = {3},

pages = {565-578},

publisher = {Société Arithmétique de Bordeaux},

title = {The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.},

url = {http://eudml.org/doc/275722},

volume = {25},

year = {2013},

}

TY - JOUR

AU - Harrington, Joshua

AU - Vincent, Andrew

AU - White, Daniel

TI - The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.

JO - Journal de Théorie des Nombres de Bordeaux

DA - 2013/11//

PB - Société Arithmétique de Bordeaux

VL - 25

IS - 3

SP - 565

EP - 578

AB - In this paper we investigate the factorization of the polynomials $f(x)x^n+g(x)\in \mathbb{Z}[x]$ in the special case where $f(x)$ is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that $f(x)$ is monic and linear.

LA - eng

KW - polynomials; trinomials; irreducible; factorization; irreducibility criteria; factorization of polynomials; quadratic polynomial

UR - http://eudml.org/doc/275722

ER -

## References

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- A. Brauer, On the irreducibility of polynomials with large third coefficient II. Amer. J. Math. 73 (1951), 717–720. Zbl0042.25201MR43131
- J.B. Conway, Functions of One Complex Variable. New York: Springer-Verlag. Zbl0887.30003MR503901
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- J. Harrington, On the Factorization of the Trinomials ${x}^{n}+c{x}^{n-1}+d$. Int. J. Number Theory 08 (2012), 1513–1518. Zbl1293.12003MR2965763
- A. Schinzel, On the reducibility of polynomials and in particular of trinomials. Acta. Arith. 11 (1965), 1–34. Zbl0196.31104MR180549
- A. Schinzel, Reducibility of polynomials and covering systems of congruences. Acta. Arith. 13 (1967), 91–101. Zbl0171.00701MR219515

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