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Is it possible to write $$64x^6-112x^4+56x^2-7$$ in linear factors?

If so, what are they?

(Finding it really difficult to ask this question!!)

Martin Sleziak
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maths
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    As a possible start, substitute $u = x^2$ and reduce it to the cubic $64u^3 - 112u^2 + 56 u - 7$. –  Nov 27 '13 at 15:59
  • Are you dealing with $\sin\frac{r\pi}7$ for integer $r$? If yes, see my answers here( http://math.stackexchange.com/questions/470614/find-the-value-of-textrmcosec2-left-frac-pi7-right-textrmcosec2-left) and here(http://math.stackexchange.com/questions/311781/method-to-find-sin-2-pi-7). Also have a look into http://mathworld.wolfram.com/TrigonometryAnglesPi7.html – lab bhattacharjee Nov 27 '13 at 16:08
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    Have you learned Eisenstein's Criterion? – Bill Kleinhans Nov 27 '13 at 20:26

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Using the Rational Root Theorem, after a bit of testing, we see that there are no rational roots. So you won't find "easily accessible" factors of the form $x-r$, where $ r \in \mathbb {Q} $. Also, see here.

Ahaan S. Rungta
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