How do you factor # (x^3)- 100 = 0#?

1 Answer
Jan 19, 2018

Answer:

#(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0#

Explanation:

We could use the fact that #a^3-b^3=(a-b)(a^2+ab+b^2)#

So we could rewrite #x^3-100=0# as
#x^3-(root 3 100)^3=0=>(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0#

To find the values of #x#, you could solve the following equations:
#x-root 3 100=0# and #x^2+xroot3 100+ (root 3 100)^2=0#.