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#1 2006-12-05 08:18:21

NewGuy24
Member
Registered: 2006-12-05
Posts: 2

Need help factoring this!

Had a easy math test, but couldn't get the bonus.

Factor Completely:  X^6-9X^4-X^2+9

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#2 2006-12-05 08:36:26

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: Need help factoring this!

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#3 2006-12-05 09:51:49

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Need help factoring this!




Why did the vector cross the road?
It wanted to be normal.

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#4 2006-12-05 10:10:16

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: Need help factoring this!

Looks like I didn't go far enough.   Thanks Mathsyperson.   But why did you break down the (x^4 - 1) the way you did?   

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#5 2006-12-05 12:36:11

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Need help factoring this!

Oops, looks like I didn't go far enough either. I should have seen that double-difference of squares thing. Ah well. We make a good team. smile


Why did the vector cross the road?
It wanted to be normal.

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#6 2006-12-05 17:49:39

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Need help factoring this!

When given a problem on a test, you can use a little trick to cheat, sort of.  It also happens to be useful when factoring polynomials over integers mod n.

Simply do the following:

Take P(x) (your polynomial) and plug in 1.  If P(1) = 0, then you can take (x-1) out of your polynomial.  Try P(2), P(3), P(-1), etc.

But remember, you can really only use this trick because teachers give nice numbers.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#7 2006-12-09 04:27:56

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Need help factoring this!

And another - the degrees of  x are only even. So you can plug y=x^2 and the degree of the equation will become form 6 to 3, which is some helpful simplification.


IPBLE:  Increasing Performance By Lowering Expectations.

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