How do you factor #27x ^3 + 216#?

1 Answer
Dec 5, 2015

Answer:

#27x^3+216 = 27(x+2)(x^2-2x+4)#

Explanation:

Both terms in the original expression have a factor of #27# which can be extracted as a factor of the expression.

The remaining factor #(x^3+8)=(x^3+2^3)# is of the form
#color(white)("XXX")(x^3+a^3)#
which we know has a factors #(x+a)# and #(x^2-ax+a^2)#
or in this case
#color(white)("XXX")(x^3+8)=(x+2)(x^2-2x+4)#

By checking the discriminant of #(x^2-2x+4)#
#color(white)("XXX")(-2)^2+4(1)(4) < 0 rArr # no further Real roots