How do you factor $x^4-6x^2-16$ ?

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Answer 1 · 2015-06-07T12:52:10

$x^4-6x^2-16$

$= (x^2)^2-6(x^2)-16$

$=(x^2-8)(x^2+2)$

$=(x-sqrt(8))(x+sqrt(8))(x^2+2)$

$=(x-2sqrt(2))(x+2sqrt(2))(x^2+2)$

$(x^2+2)$ has no simpler factors with real coefficients,

since $(x^2+2) >= 2$ so $x^2+2 = 0$ has no roots for all $x in RR$ .

How do you factor x^4-6x^2-16x^4-6x^2-16?