How do you factor completely #2x^4 -14x^2 +24#?

1 Answer
Jul 27, 2016

Answer:

#color(green)(2(x-sqrt(3))(x+sqrt(3))(x-2)(x+2))#

Explanation:

Temporally replacing #x^2# with #a#
#2x^4-14x^2+24# becomes #2a^2-14a+24#

#2a^2-14a+24#
#color(white)("XXX")=2(a^2-7a+12)#

#color(white)("XXX")=2(a-3)(a-4)#

Restoring #x^2# in place of #a#
#color(white)("XXX"){: ((a-3)=(x^2-3),color(white)("XX"),(a-4)=(x^2-4)), (color(white)("X")=(x-sqrt(3))(x+sqrt(3)),,color(white)("X")=(x-2)(x+2)) :}#

So
#2x^4-14x^2+24#
#color(white)("XXX")=color(green)(2(x-sqrt(3))(x+sqrt(3))(x-2)(x+2))#