## Number Of Real Roots Of A Quintic Polynomial – Math.stackexchange.com

Online Web Tricks · 13:10 01 Feb 2018
Obtain the number of real roots of the following quintic polynomial $$f(x)= x^5+x^3-2x+1$$ My approach: First, on seeing the polynomial, it should be clear that it is continuous. Also, ...fr… Read More

## Division Of One Polynomial By Another. – Math.stackexchange.com

Online Web Tricks · 12:40 02 Feb 2018
How is this done? For example, how would one simplify this: $$\frac{x^3-12x^2+0x-42}{x^2-2x+1}$$ I can do it with long division, but it never makes intuitive sense to me. Either an explanati… Read More

## How To Show That The Following Function Isn't A Polynomial Over Q? – Mathoverflow.net

Online Web Tricks · 20:51 11 Dec 2017
Enumerate the rationals as $b_1,b_2,\dots$ and define the (set) function: $$f(x) = (x-b_1)^2 + (x-b_1)^2(x-b_2)^2 + \dots.$$ At any particular $x$, only finitely many terms are non zero so t… Read More

## Why Can’t You Use Cyclotomic Polynomials To Factor Big Numbers Really Quickly? – Mathoverflow.net

Online Web Tricks · 02:36 13 Feb 2018
Two simple remarks: The polynomial $x^k-1$ can be factorised over the integers as a product of (irreducible) cyclotomic polynomials: $$x^k-1 = \prod_{d|k}\Phi_d(x).$$ If we choose $k$ to be… Read More
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