# How do you factor completely #x^3+1/8#?

##### 1 Answer

Mar 3, 2016

#### Answer:

#x^3+1/8=(x+1/2)(x^2-1/2x+1/4)#

#### Explanation:

Both

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

with

#x^3+1/8#

#=x^3+(1/2)^3#

#=(x+1/2)(x^2-x(1/2)+(1/2)^2)#

#=(x+1/2)(x^2-1/2x+1/4)#

The remaining quadratic factor has no simpler factors with Real coefficients, but we can factor it if we allow Complex coefficients:

#=(x+1/2)(x+1/2omega)(x+1/2omega^2)#

where