How do you factor # 2x^6-3x^4#?

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Answer 1 · 2015-06-15T04:03:16

Factor out the greatest common factor #x^4# to get #x^4(2x^2-3)#.

Factor out the GCF #x^4#.

#2x^6-3x^4# =

#x^4(2x^2-3)#

Answer 2 · 2015-06-15T06:46:44

#2x^6-3x^4 = x^4(2x^2-3) = x^4(sqrt(2)x-sqrt(3))(sqrt(2)x+sqrt(3))#

First separate out the common factor #x^4# to get:

#2x^6-3x^4 = x^4(2x^2-3)#

The remaining quadratic factor can be treated as a difference of squares with irrational coefficients:

#2x^2-3 = (sqrt(2))^2x^2-(sqrt(3))^2#

#=(sqrt(2)x)^2 - (sqrt(3))^2#

#=(sqrt(2)x-sqrt(3))(sqrt(2)x+sqrt(3))#

using the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#