document.write( "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! \n" ); document.write( "

Algebra.Com's Answer #357512 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Factoring leads you to the answer
\n" ); document.write( " $\"256n%5E3+=+30976n\"$ ---> $\"256n%5E3-30976n=0\"$ ---> $\"256n%28n%5E2-121%29=0\"$ ---> $\"256n%28n%2B11%29%28n-11%29=0\"$
\n" ); document.write( "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.
\n" ); document.write( "I recognized $\"n%5E2=121=n%5E2-11%5E2\"$ as the difference of two squares after that.
\n" ); document.write( "The full factorization tells you that the solutions to the equation will be
\n" ); document.write( " $\"n=0\"$ , $\"n=-11\"$ , and $\"n=11\"$ , the values that make the factors zero. \n" ); document.write( "

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