How do you factor x^3-27?
1 Answer
Mar 15, 2016
Use the difference of cubes identity to find:
x^3-27 = (x-3)(x^2+3x+9)
Explanation:
Both
a^3-b^3 = (a-b)(a^2+ab+b^2)
with
x^3-27
=x^3-3^3
=(x-3)(x^2+x(3) + 3^2)
=(x-3)(x^2+3x+9)
This is as far as you can go with Real coefficients. If you allow Complex coefficients then you can factor this a little further:
=(x-3)(x-3omega)(x-3omega^2)
where