# How do you factor #x^3 - 16#?

##### 1 Answer

Apr 7, 2016

#### Answer:

#x^3-16#

#=(x-2 root(3)(2))(x^2+2 root(3)(2) x + 4 root(3)(4))#

#=(x-2 root(3)(2))(x-2 root(3)(2) omega)(x-2 root(3)(2) omega^2)#

#### Explanation:

Use the difference of cubes identity:

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

with

So:

#x^3-16 =x^3-(2 root(3)(2))^3#

#=(x-2 root(3)(2))(x^2+2 root(3)(2) x + 4 root(3)(4))#

This is as far as we can go with Real coefficients, but if you allow Complex coefficients then this can be further factored as:

#=(x-2 root(3)(2))(x-2 root(3)(2) omega)(x-2 root(3)(2) omega^2)#

where