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1) "Factoring" -- As to factoring algebra 2factor
Function: verb
Inflected Form(s): factored; factoring /-t(&-)ri[ng]/
intransitive verb : to work as a factor
transitive verb
1 : to resolve into factors
2 a : to include or admit as a factor -- used with in or into <factor inflation into our calculations> b : to exclude as a factor -- used with out
- factorable /-t(&-)r&-b&l/ adjective Pronunciation Symbols
In mathematics, factorization 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. The opposite of factorization is expansion. This is the process of multiplying together factors to recreate the original, "expanded" polynomial. 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. - 1 Prime factorization of an integer
- 2 Factoring a quadratic polynomial
- 2.1 Perfect square trinomials
- 2.2 Table method
- 3 Sum/difference of two squares
- 4 Sum/difference of two cubes
- 5 Factoring by grouping
- 6..."
2) "Algebra" -- As to factoring algebra algebra
Pronunciation: 'al-j&-br&
Function: noun
Etymology: Medieval Latin, from Arabic al-jabr, literally, the reduction
1 : a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic
2 : any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations often analogous to those of arithmetic -- compare BOOLEAN ALGEBRA
- algebraist /-"brA-ist/ noun Pronunciation Symbols
Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī titled (in Arabic كتاب الجبر والمقابلة )Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations. Together with geometry, analysis, and number theory, algebra is one of the several main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots. Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields. - 1 Classification
- 2 Elementary algebra
- 3 Abstract algebra
- 3.1 Groups
- 3.2 Rings and fields—structures with two binary operations
- 4 Algebras
- 5 History
- 6 References
- 7 See also
- 8 References
- 9 External links
| Linear algebra lecture about determinants and inverse matrices. Algebra may be divided roughly into the following categories: - Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and var..."
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