SOLUTION: What is the factorization of 729x^15 + 1000? I really have no clue where to even start on this one...

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the factorization of 729x^15 + 1000? I really have no clue where to even start on this one...      Log On


   

Question 967010: What is the factorization of 729x^15 + 1000? I really have no clue where to even start on this one...
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=9x%5E5
Then,
u%5E3=729x%5E15
So,
u%5E3%2B1000 is now a sum of two cubes.
u%5E3%2B1000=%28u%2B10%29%28u%5E2-10u%2B100%29
729x%5E15%2B1000=%289x%5E5%2B10%29%28%289x%5E5%29%5E2-10%289x%5E5%29%2B100%29
729x%5E15%2B1000=%289x%5E5%2B10%29%2881x%5E10-90x%5E5%2B100%29