How do you factor #x^4+6x^2-7# completely?

1 Answer
George C.
Jun 22, 2016

#x^4+6x^2-7#

#=(x^2+7)(x-1)(x+1)#

#=(x-sqrt(7)i)(x+sqrt(7)i)(x-1)(x+1)#

Explanation:

You can factor it as a "quadratic in #x^2#" then factor each of the quadratic factors:

#x^4+6x^2-7#

#=(x^2)^2+6(x^2)-7#

#=(x^2+7)(x^2-1)#

#=(x^2+7)(x-1)(x+1)#

#=(x-sqrt(7)i)(x+sqrt(7)i)(x-1)(x+1)#

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