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Student Support Forum: 'Polynomial factorization by roots?' topicStudent Support Forum > General > "Polynomial factorization by roots?"

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Author Comment/Response
yehuda
12/28/12 11:39am

In Response To 'Re: Re: Polynomial factorization by roots?'
---------
If Solve can find the roots of the polynomial you can use it without guessing that you need Extension->I

for your specific example
p = x^4 + 2 x^2 + 1;
Times @@ Subtract @@@ Flatten@Solve[p == 0, x]
returns what you need
now slower
Solve[p == 0, x]
returns
{{x -> -I}, {x -> -I}, {x -> I}, {x -> I}}
To omit the internal lists you use Flatten
Flatten[Solve[p == 0, x]] (or Flatten@Solve[p==0,x])

Then you replace the x->I etc to x-I etc using Apply at level 1 with the shortcut of @@@
Subtract @@@ Flatten@Solve[p == 0, x]
returns
{I + x, I + x, -I + x, -I + x}
Now replace the outermost head which is a list with Times for multiplication
This is again Apply but at level 0 (replacing the outermost head) using the shortcut @@

Without the shorthand notation this would be
Apply[Times, Apply[Subtract, Flatten[Solve[p == 0, x]], 1]]

HTH
yehuda

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Subject (listing for 'Polynomial factorization by roots?')
Author Date Posted
Polynomial factorization by roots? Gandalf Saxe 12/11/12 11:08am
Re: Polynomial factorization by roots? Nasser M. Ab... 12/12/12 08:07am
Re: Polynomial factorization by roots? Gandalf 12/18/12 08:58am
Re: Polynomial factorization by roots? Steve Keeley 12/25/12 7:44pm
Re: Re: Polynomial factorization by roots? Steve Keeley 12/26/12 7:30pm
Re: Polynomial factorization by roots? Steve Keeley 12/26/12 7:48pm
Re: Re: Polynomial factorization by roots? Gandalf Saxe 12/28/12 05:36am
Re: Re: Re: Polynomial factorization by roots? yehuda 12/28/12 11:39am
Re: Re: Re: Polynomial factorization by roots? Steve Keeley 12/28/12 12:11pm
Re: Re: Re: Polynomial factorization by roots? Steve Keeley 12/28/12 1:02pm
Re: Re: Re: Re: Polynomial factorization by roo... yehuda 12/29/12 00:17am
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