( )(x2 ( )3 + 73 ( ( )2 (
( )(x2 ( )3 + 73 ( ( )2 (

The Rational Zero Test The ultimate objective for this section of the
The Rational Zero Test The ultimate objective for this section of the

1.2 Properties of Real Numbers
1.2 Properties of Real Numbers

... So the number 5 is an Natural number, a whole number, an integer, a rational 25 number and a Real number same as The number – 176 would be an integer, a rational number and a Real Number ...
Number Fields
Number Fields

Solving Linear Equations Review Strategy: 1) Simplify both sides of
Solving Linear Equations Review Strategy: 1) Simplify both sides of

Galois Field in Cryptography
Galois Field in Cryptography

The Fundamental Theorem of Algebra - A History.
The Fundamental Theorem of Algebra - A History.

Solutions - Penn Math
Solutions - Penn Math

Supplemental Questions Packet
Supplemental Questions Packet

Document
Document

Complex Numbers, Polynomials, and Symmetry
Complex Numbers, Polynomials, and Symmetry

Classroom “RULES” Chart – recording of students generalizing of
Classroom “RULES” Chart – recording of students generalizing of

Study Guide
Study Guide

Book sketch for High School teachers
Book sketch for High School teachers

Prime Numbers and Prime Factorization
Prime Numbers and Prime Factorization

NxG Algebra II CSO List.xlsx
NxG Algebra II CSO List.xlsx

Diophantine Aproximations
Diophantine Aproximations

Cryptography Midterm Solutions
Cryptography Midterm Solutions

Divide and Conquer Polynomial Long Division
Divide and Conquer Polynomial Long Division

Lecture 6 1 Multipoint evaluation of a polynomial
Lecture 6 1 Multipoint evaluation of a polynomial

... • Resultant of two polynomials. ...
DS Lecture 9
DS Lecture 9

... Example: Test if 139 and 143 are prime. List all primes up to n and check if they divide the numbers. 2: Neither is even 3: Sum of digits trick: 1+3+9 = 13, 1+4+3 = 8 so neither divisible by 3. 5: Don’t end in 0 or 5 7: 140 divisible by 7 so neither div. by 7 11: Alternating sum trick: 1-3+9 = 7 so ...
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let

MATH 311-02 Midterm Examination #2 solutions 1. (20 points
MATH 311-02 Midterm Examination #2 solutions 1. (20 points

On the Sum of Square Roots of Polynomials and related problems
On the Sum of Square Roots of Polynomials and related problems

... Theorem 1.4 (Sum of square root of ‘polynomial integers’). Suppose S = i=1 δi ai (δi ∈ {+1, −1}) such that every positive integer ai is of the form ai = X di + bi1 · X di −1 + . . . + bidi (di > 0), where X is a positive real number and bij are integers. Let B = maxi,j {|bij |} and d = maxi {di }. I ...
The calculation of the degree of an approximate greatest common
The calculation of the degree of an approximate greatest common

Eisenstein's criterion

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers—that is, for it to be unfactorable into the product of non-constant polynomials with rational coefficients.This criterion is not applicable to all polynomials with integer coefficients that are irreducible over the rational numbers, but it does allow in certain important cases to prove irreducibility with very little effort. It may apply either directly or after transformation of the original polynomial.This criterion is named after Gotthold Eisenstein. In the early 20th century, it was also known as the Schönemann–Eisenstein theorem because Theodor Schönemann was the first to publish it.