How do you factor completely #8z^3 +27#?
1 Answer
Aug 21, 2016
Explanation:
The sum of cubes identity can be written:
#a^3+b^3=(a+b)(a^2-ab+b^2)#
We use this with
#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#
