/sci/ - Science & Math » Thread #10946514

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Anonymous Thu 05 Sep 16:55:01 2019 No.10946514 View Reply Original Report

Quoted By: >>10946518 >>10946519 >>10946772 >>10946773

factor this shit $x^10 + x^5 + 1$

Anonymous

Anonymous Thu 05 Sep 2019 16:55:56 No.10946518 Report

Quoted By:

>>10946514
No

Anonymous

Anonymous Thu 05 Sep 2019 16:56:17 No.10946519 Report

Quoted By:

>>10946514
$x^{10} + x^5 +1$

Anonymous

Anonymous Thu 05 Sep 2019 18:53:37 No.10946772 Report

Quoted By:

>>10946514
Just use quadratic formula and fuck off.

Anonymous

Anonymous Thu 05 Sep 2019 18:59:54 No.10946773 Report

Quoted By:

>>10946514
$x^{10} + x^5 + 1 = u^2 + u +1$
Where
$u = x^5$

You can even fine the 10 complex roots .

Anonymous

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Anonymous Thu 05 Sep 2019 19:04:07 No.10946784 Report

Quoted By:

$x^{10} + x^5 + 1 = \frac{x^{15} - 1}{x^5 - 1}$
Simple answer: notice that $x^3 - 1 | x^{15} - 1$ . So, taking gcd of $x^{10} + x^5 + 1$ and $x^3 - 1$ will give you a nontrivial factorisation.
Other answer: problem is trivial if you know about cyclotomic polynomials.

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