SOLUTION: I cannot figure out how to do this problem, 256n^3 = 30,976n, my teacher says that we need 3 different answers, and I have no clue where to begin with this. Thanks for your help in

Algebra ->  Exponents -> SOLUTION: I cannot figure out how to do this problem, 256n^3 = 30,976n, my teacher says that we need 3 different answers, and I have no clue where to begin with this. Thanks for your help in      Log On


   

Question 548753: I cannot figure out how to do this problem, 256n^3 = 30,976n, my teacher says that we need 3 different answers, and I have no clue where to begin with this. Thanks for your help in advance!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Factoring leads you to the answer
256n%5E3+=+30976n ---> 256n%5E3-30976n=0 ---> 256n%28n%5E2-121%29=0 ---> 256n%28n%2B11%29%28n-11%29=0
I just asked my calculator, and found that 30976%2F256=121, so I pulled 256n out as a common factor. I guess I could have divided both sides of the equation by 256 at the start instead.
I recognized n%5E2=121=n%5E2-11%5E2 as the difference of two squares after that.
The full factorization tells you that the solutions to the equation will be
n=0, n=-11, and n=11, the values that make the factors zero.