How do you factor 27x ^3 + 216?

1 Answer
Dec 5, 2015

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