Question

Using complete sentences, explain how you would factor completely x^9 –27.

Please Help!!

Answer 1

here we can use the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2) by manipulating x^9 - 27 as follows

x^9 - 27 = (x^3)^3 - (3)^3
using above identity we get
(x^3 - 3)[(x^3)^2 + (x^3)(3) + (3)^2]
(X^3 - 3)(x^6 + 3x^3 + 9)