• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Solutions - CEMC - University of Waterloo
Solutions - CEMC - University of Waterloo

Unit 3B Notes: Graphs of Polynomial Functions
Unit 3B Notes: Graphs of Polynomial Functions

Math 1420 Homework 9
Math 1420 Homework 9

... Math 1420 Homework 9 ...
Gaussian Integers - Clarkson University
Gaussian Integers - Clarkson University

... The Gaussian integers are defined as the set of all complex numbers with integral coefficients. Under the familiar operations of complex addition and multiplication, this set forms a subring of the complex numbers, denoted by Z[i]. First introduced by Gauss, these relatives of the regular integers p ...
6.2 notes
6.2 notes

Find the greatest common monomial factor Solve an equation by
Find the greatest common monomial factor Solve an equation by

Algebra II (10) Semester 2 Exam Outline – May 2015 Unit 1
Algebra II (10) Semester 2 Exam Outline – May 2015 Unit 1

2016.17, Algebra II, Quarter 2
2016.17, Algebra II, Quarter 2

1.4 Rectangles and Factor Pairs Two whole #s that are multiplied to
1.4 Rectangles and Factor Pairs Two whole #s that are multiplied to

Algebra 2: Harjoitukset 2. A. Definition: Two fields are isomorphic if
Algebra 2: Harjoitukset 2. A. Definition: Two fields are isomorphic if

x - ClassZone
x - ClassZone

Lecture Thursday
Lecture Thursday

[10.1]
[10.1]

... polynomial. Show that, on one hand, Φn (q) divides q n − q, but, on the other hand, this is impossible unless n = 1. Thus D = k. ) First, the center k of D is defined to be k = center D = {α ∈ D : αx = xα for all x ∈ D} We claim that k is a field. It is easy to check that k is closed under addition, ...
Math 095 – Formulas
Math 095 – Formulas

The Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra

5.6 – Quadratic Equations and Complex Numbers
5.6 – Quadratic Equations and Complex Numbers

Pacing Guide: Secondary Math II, Instructional Block 2, Part A
Pacing Guide: Secondary Math II, Instructional Block 2, Part A

ALGEBRAIC  NUMBER  THEORY
ALGEBRAIC NUMBER THEORY

2016-Complex-Numbers_Exercise-Sheet
2016-Complex-Numbers_Exercise-Sheet

Aurifeuillian factorizations - American Mathematical Society
Aurifeuillian factorizations - American Mathematical Society

Test 2 Working with Polynomials
Test 2 Working with Polynomials

... Donkey Kong is competing in a shot-put challenge at the Olympics. His throw can be modeled by the function h(t) = -5t2 + 8.5t + 1.8, where h is the height, in metres, of a shot-put t seconds after it is thrown. Determine the remainder when h(t) is divided by (t – 1.4). What does this value represent ...
Name: Exam 2 Directions: You must show all of your work for full
Name: Exam 2 Directions: You must show all of your work for full

univariate case
univariate case

The Rational Zero Theorem
The Rational Zero Theorem

Math 594, HW7
Math 594, HW7

< 1 ... 216 217 218 219 220 221 222 223 224 ... 230 >

Factorization



In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report