Can someone teach me how to do radical factorization? Or introduce a good website which teaches how to do it..

Thanks Bro

Printable View

- March 11th 2006, 06:15 PMguessradical factorization
Can someone teach me how to do radical factorization? Or introduce a good website which teaches how to do it..

Thanks Bro - March 11th 2006, 06:26 PMThePerfectHackerQuote:

Originally Posted by**guess**

Such as,

- March 12th 2006, 01:59 AMguess
I mean something more complication such as 1/(3+X^5)

- March 12th 2006, 02:01 AMguess
Or more complex like 1/(1+x^6)

- March 12th 2006, 07:21 AMAradesh
I think you are referring to your integration thread when was factorized to by TD.

you can do this since if you have

it can be expressed in the form if you expand the brackets you will see that it is indeed

now how would you think to do this?

well it comes from the difference of two squares where if you have this is

if we think of our x in the difference of two squares as (a+b) then (a+b)^2 is going to come out in the result somewhere, and (a+b)^2 = a^2 + b^2 + 2ab

now this has a^2+b^2 in it but it is 2ab too much.

however if we choose the right y we can get the 2ab to disappear. for instance

this expands to

so if we choose such that:

then:

so

we get:

so from the original

if we say a = 1 and b = x^2 it factorizes to:

- March 12th 2006, 07:27 AMAradesh
so in your integration thread you had

and as shown the bottom part factorizes like so

then this was then decomposed with partial fractions to the form (i'll take td's word):

which is what theperfecthacker was talking about. - March 12th 2006, 07:44 AMAradesh
it is worth noting however that

is difficult to factorize because it is in the form

factorizing things in the form for all odd k

so where p is a prime number not equal to 2 is factorizable into the form above. as the rest of the prime numbers are odd.

so for even k, if k = rp where p is a prime factor other than 2 then:

and since p is odd, this factorizes also, to:

so this only leaves things in the form

which don't factorize nicely.

does not factorize

if

then

so does not factorize either.

this is useful in searching for fermat primes, so we only know to look for primes in the form since all other indices factorize. - March 13th 2006, 01:30 AMguess
thanks alot aradesh... You have done a Great help...