document.write( "Question 1075873: Solve via direct proof:
\n" ); document.write( "n^5 - 64n^3 - n^2 ∈ Θ (n^5)\r
\n" ); document.write( "\n" ); document.write( "I'm not exactly sure what to do. I factored the left side:
\n" ); document.write( "n^2 (n^3 - 64n - 1)
\n" ); document.write( "and the right:
\n" ); document.write( "Θ (n^2)(n^3)
\n" ); document.write( "to get:
\n" ); document.write( "n^2 (n^3 - 64n - 1) ∈ Θ (n^2)(n^3)\r
\n" ); document.write( "\n" ); document.write( "What do I do now?\r
\n" ); document.write( "\n" ); document.write( "Also, is there a paid tutor online that could help me with a few others (that are even more difficult?) ~J
\n" ); document.write( "

Algebra.Com's Answer #690525 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1.  Could you please to share the secret with us: what is Θ (n^5) ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.  Do not panic.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "      Simply post your problems, correctly and accurately formulated.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3.  You are at the right place and in good hands.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------
\n" ); document.write( "comment from student: Thank you. It just says \"Use a direct proof to find constants that satisfy the definition of Θ (n^5)\"
\n" ); document.write( "Not sure where to go.
\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "My response:  Honestly,  I expected to get another answer.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                      This one DOES NOT make us closer to understanding.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );