document.write( "Question 806049: Please help me solve this problem:\r
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Algebra.Com's Answer #839086 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Please help me solve this problem:
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\n" ); document.write( "\n" ); document.write( "        I will show you another, nontraditional way to solve the problem, \r
\n" ); document.write( "\n" ); document.write( "        which is  (I am  100%  sure)  absolutely unexpected to you   (and to many others).\r
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document.write( "Start from this innocent transformation\r\n" );
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document.write( "    x^3 - 6 = (x^3 - 8) + 2.\r\n" );
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document.write( "For the parentheses in the right side, use well known decomposition\r\n" );
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document.write( "    a^3 - b^3 = (a-b)*(a^2 + ab + b^2).\r\n" );
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document.write( "Take here a= x,  b= 2.  You will get then\r\n" );
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document.write( "    x^3 - 8 = (x-2)*(x^2 + 2x + 4).\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( "    x^3 - 6 = (x^3 - 8) + 2 = (x-2)*(x^2 + 2x + 4) + 2.\r\n" );
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document.write( "It means that \r\n" );
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document.write( "    \"%28x%5E3-6%29%2F%28x-2%29\" = x^2 + 2x + 4  with the remainder of 2.\r\n" );
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document.write( "ANSWER.   \"%28x%5E3-6%29%2F%28x-2%29\" = x^2 + 2x + 4  with the remainder of 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is good solution to show it at the local school  Math circle.\r
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\n" ); document.write( "\n" ); document.write( "The students will be positively shocked (= overwhelmed; = stunned) :   a deafening effect is guaranteed.\r
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\n" ); document.write( "\n" ); document.write( "Notice that I did not make any division for it - neither polynomial nor synthetic.\r
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\n" ); document.write( "\n" ); document.write( "I extracted the solution from the air,  using the method called  \" focus-pocus \".\r
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\n" ); document.write( "\n" ); document.write( "After such an  \" exercise \",  the students will know and understand Math  \" in two times better \"  than before it.\r
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\n" ); document.write( "\n" ); document.write( "And they will have a stimulus to learn it better.\r
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