## Factor Theorem Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

... 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

## Remainder Theorem

## Euler's theorem

## Stolper–Samuelson theorem

## Rybczynski theorem

## Unique Factorization Theorem

## source compression factor

## factorize

## greatest common factor

## synthetic division

## source coding

## Paul A. Samuelson

## tactical voting

## apportionment

## factorize Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

...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.)

...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.)

...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.)

...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.)

...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...