Mathematics-Online lexicon: Factor out

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	Mathematics-Online lexicon:
	Factor out

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

An equation of the form

$\displaystyle a_nx^n+a_{n-1}x^{n-1}+...+a_{n-m+1}x^{n-m+1}+a_{n-m}x^{n-m}=0 \textnormal{, } \qquad a_n\not=0 \qquad n>m$

can be solved by factoring out the smallest power $x^{n-m}$ that occurs in the term.

$\displaystyle x^{n-m}(a_nx^{m}+a_{n-1}x^{m-1}+...+a_{n-m+1}x+a_{n-m})=0 \textnormal{, } \qquad a_n\not=0$

As a product is zero iff at least one the factors is zero, you get the (

)-fold solution of the equation

$\displaystyle x=0.$

The further

solution can be calculated by solving the term in the brackets

$\displaystyle a_nx^{m}+a_{n-1}x^{m-1}+...+a_{n-m+1}x+a_{n-m}=0.$

(Authors: Jahn/Knödler)

automatically generated 7/ 8/2004