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Factor Theorem

The following result, which is an immediate consequence of the Remainder Theorem: Theorem Let f(x) be a polynomial. Then x−h is a factor of f(x) if and only if f(h)=0. ...

Factor Theorem

Factor Theorem   Quick reference

The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

... Theorem The following result, which is an immediate consequence of the remainder theorem : Theorem Let f ( x ) be a polynomial. Then x − h is a factor of f ( x ) if and only if f ( h )=0. The theorem is valuable for finding factors of polynomials. For example, to factorize 2 x 3 +3 x 2 −12 x −20, look first for possible factors x − h , where h is an integer. Here h must divide 20. Try possible values for h , and calculate f ( h ). It is found that f (−2)=−16+12+24−20=0, and so x +2 is a factor. Now divide the polynomial by this factor to...

Factor Theorem

Factor Theorem  

The following result, which is an immediate consequence of the Remainder Theorem:TheoremLet f(x) be a polynomial. Then x−h is a factor of f(x) if and only if f(h)=0.The theorem is valuable for ...
Remainder Theorem

Remainder Theorem  

The following result about polynomials:TheoremIf a polynomial f(x) is divided by x−h, then the remainder is equal to f(h).It is proved as follows. Divide the polynomial f(x) by x−h to get a quotient ...
Euler's theorem

Euler's theorem  

Iff(x1, …, xn)is homogeneous of degree n thenOne use of the theorem is to demonstrate that with constant returns to scale and competitive factor markets the total payment to factors equals the ...
Stolper–Samuelson theorem

Stolper–Samuelson theorem  

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Overview Page
A result stating that in a competitive world economy with constant returns to scale and two factors of production, a rise in the relative price of a good will lead to an increase in the return to the ...
Rybczynski theorem

Rybczynski theorem  

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A proposition concerning the results of increasing only one factor of production. The proposition, named after its originator, concerns a two-good, two-factor economy with constant returns to scale, ...
Unique Factorization Theorem

Unique Factorization Theorem  

The process of writing any positive integer as the product of its prime factors is probably familiar; it may be taken as self-evident that this can be done in only one way. Known as the Unique ...
source compression factor

source compression factor  

The ratio of message lengths before and after source coding (which is generally intended to make messages shorter). See also source coding theorem.
factorize

factorize  

To represent a number, matrix or polynomial as a product of factors. Of particular importance is the Unique Factorization Theorem.
greatest common factor

greatest common factor  

For two non-zero integers a and b, any integer that is a divisor of both is a common divisor. Of all the common divisors, the greatest is the greatest common divisor (or g.c.d.), denoted by (a, b). ...
synthetic division

synthetic division  

A method of finding the quotient and remainder when a polynomial f(x) is divided by a factor x−h, in which the numbers are laid out in the form of a table. The rule to remember is that, at each step, ...
source coding

source coding  

The use of variable-length codes in order to reduce the number of symbols in a message to the minimum necessary to represent the information in the message, or at least to go some way toward this, ...
Paul A. Samuelson

Paul A. Samuelson  

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(1915–2009)US economist who won the 1970 Nobel Prize for his work in economic analysis and methodology, particularly the use of mathematical tools and derivation of new theorems.Born in Indiana, ...
tactical voting

tactical voting  

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In a first‐past‐the‐post electoral system a vote is tactical when it is cast for a candidate that the voter believes is more likely to win than their preferred candidate, to best influence who wins ...
apportionment

apportionment  

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Allocation of seats to regional units, or to parties under systems of proportional representation.Territorial apportionment is usually a process of adjusting the seats allocated to each unit to ...
factorize

factorize   Quick reference

The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...To represent a number, matrix or polynomial as a product of factors. Of particular importance is the unique factorization theorem...

remainder theorem

remainder theorem   Quick reference

The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...theorem The following result about polynomials: Theorem If a polynomial f ( x ) is divided by x − h , then the remainder is equal to f ( h ). It is proved as follows. Divide the polynomial f ( x ) by x − h to get a quotient q ( x ) and a remainder which will be a constant, r . This means that f ( x )=( x − h ) q ( x )+ r . Replacing x by h in this equation gives r = f ( h ), thus proving the theorem. An important consequence of the remainder theorem is the Factor Theorem...

source compression factor

source compression factor   Quick reference

A Dictionary of Computer Science (7 ed.)

Reference type:
Subject Reference
Current Version:
2016

...compression factor The ratio of message lengths before and after source coding (which is generally intended to make messages shorter). See also source coding theorem...

Stolper–Samuelson theorem

Stolper–Samuelson theorem   Quick reference

A Dictionary of Economics (5 ed.)

Reference type:
Subject Reference
Current Version:
2017
Subject:
Social sciences, Economics
Length:
110 words

...theorem A result stating that in a competitive world economy with constant returns to scale and two factors of production, a rise in the relative price of a good will lead to an increase in the return to the factor which is used most intensively in the production of that good, and to a fall in the return to the other factor. The theorem, named after its originators, is used to explain the consequences of opening an economy to trade, or of introducing trade protection. In either case, the relative prices of goods will change, and the theorem...

Euler’s theorem

Euler’s theorem   Quick reference

A Dictionary of Economics (5 ed.)

Reference type:
Subject Reference
Current Version:
2017
Subject:
Social sciences, Economics
Length:
202 words
Illustration(s):
4

...Euler’s theorem If f   ( x 1 , …, x n ) is homogeneous of degree λ ‎ then x 1 ∂ f ∂ x 1 + … + x n ∂ f ∂ x n = λ f ( x 1 , … , x n ) . One use of the theorem is to demonstrate that with constant returns to scale and competitive factor markets the total payment to factors equals the revenue of the firm. Assume there are two factors, capital, K , and labour, L . Constant returns to scale implies the production function is homogeneous of degree one so Euler’s theorem gives K ∂ f ∂ K + L ∂ f ∂ L = f ( K , L ) . If the price of output is p , it follows...

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