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Topic: Factoring
Replies: 52   Last Post: Jan 16, 2012 8:23 PM

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 Virgil Posts: 4,482 Registered: 1/6/11
Re: Factoring
Posted: Jan 9, 2012 7:30 PM

In article <jefpcq\$da1\$1@speranza.aioe.org>,
"John Smith" <invalid@invalid.invalid> wrote:

> Thanks everyone who replied.
>
> Having managed a basic factoring program (pun intended) I'm now wondering if
> I can extend it to list all candidate factors and then maybe extend it to
> factor any polynomial with integer coefficients using division or synthetic
> division.
>
> For my original example x^3-3x^2-4x+12 it's clear that a list of all
> combinations of (1,1,1) and (2,2,3) will include the factors if negative
> numbers are also included.
>
> For my second example 24x^3+26x^2-13x-10 factors as (2x+1)(3x-2)(4x+5)
> 24 factors as 2,2,2,3 and 10 factors as 2,5 but the factors of 24 also have
> to be considered as 2*2,2,3
> Would multiples of multiples have to be considered for polynomials of higher
> degree?
>
> What if the constant term is 0? Does that simply mean that such a polynomial
> has no linear factors?

A costant term of zero in a non-zero polynomial indicates that the
linear term x + 0, or merely x, is a factor.
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