How do you factor completely #8z^3 +27#?

1 Answer
Aug 21, 2016

Answer:

#8x^3+27=(2x+3)(4x^2-6x+9)#

Explanation:

The sum of cubes identity can be written:

#a^3+b^3=(a+b)(a^2-ab+b^2)#

We use this with #a=2z# and #b=3# to find:

#8x^3+27#

#=(2x)^3+3^3#

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

#=(2x+3)(4x^2-6x+9)#

Note that the remaining quadratic expression has no linear factors with Real coefficients. You can tell this from its discriminant:

#Delta = (-6)^2-4(4)(9) = 36-144 = -108 < 0#