factor x^4-x-^2-12
If this question were x^2 - x - 12 would you know how to factor it?
(x-3)(x+4)
swith the 3 and 4 (x-4)(x+3)
Those x's have to be squared. Which means you can still factor it more of course.
\[x^{4}- x^{2} - 12 = (x^{2} - 4)(x^{2}+3) = (x+2)(x-2)(x^{2}+3)\]
oh I just looked at your original equation
\[x^4-x ^{-2}-12\] is this the equation? if so you can look at the \[-x ^{-2}\] as \[\frac{ 1 }{ x^2 }\] What it ends up being is basically an irreducible factorization: but you can write it as this: \[\frac{ x^6-12x^2-1}{x^2}\]
Oh, -2 exponent.
\[x^{4}-x^{-2} - 12 = x^{4} - \frac{1}{x^{2}}- 12 = \frac{ x^{6} - 12x^{2} - 1 }{ x^{2} }\] Which yeah, isn't factorable by hand without approximation techniques. Oh well :/
i dont think it would be a -2 exponent. looks wrong to me johnny?
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