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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 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

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

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

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

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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

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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

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

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

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

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

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

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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

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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

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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 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 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 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 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 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...  View: