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#.