In this paper we investigate the factorization of the polynomials in the special case where is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that is monic and linear.
Dans cet article, nous étudions la factorisation des polynômes dans le cas particulier où est un polynôme quadratique unitaire avec discriminant négatif. Nous mentionnons également des résultats similaires dans le cas où est unitaire et linéaire.
Revised:
Published online:
DOI: 10.5802/jtnb.849
Classification: 11C08, 12E05, 26C10
Keywords: polynomials, trinomials, irreducible, factorization
@article{JTNB_2013__25_3_565_0, author = {Joshua Harrington and Andrew Vincent and Daniel White}, title = {The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {565--578}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {25}, number = {3}, year = {2013}, doi = {10.5802/jtnb.849}, zbl = {1293.11049}, mrnumber = {3179677}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.849/} }
TY - JOUR 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 PY - 2013 DA - 2013/// SP - 565 EP - 578 VL - 25 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.849/ UR - https://zbmath.org/?q=an%3A1293.11049 UR - https://www.ams.org/mathscinet-getitem?mr=3179677 UR - https://doi.org/10.5802/jtnb.849 DO - 10.5802/jtnb.849 LA - en ID - JTNB_2013__25_3_565_0 ER -
Joshua Harrington; Andrew Vincent; Daniel White. 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, Volume 25 (2013) no. 3, pp. 565-578. doi : 10.5802/jtnb.849. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.849/
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