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

##### 1 Answer

Dec 20, 2015

#### Answer:

Use the sum of cubes identity to find:

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

#### Explanation:

The sum of cubes identity may be written:

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

In our example, we have

#1+x^3#

#=1^3+x^3#

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

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

The remaining quadratic factor *complete* factorisation then you can do it with Complex coefficients:

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

or if you prefer:

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

where