document.write( "Question 1157739: The polynomial $\"x%5E8+-+1\"$ is factored as
\n" ); document.write( " $\"x%5E8+-+1+=+p_1%28x%29+%2A+p_2%28x%29\"$ .... $\"p_k%28x%29\"$ ,where each factor $\"p_i%28x%29\"$ is a non-constant polynomial with real coefficients. Find the largest possible value of k. \n" ); document.write( "

Algebra.Com's Answer #780619 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "     =  =  = .     (1)\r\n" );
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document.write( "The factor    also can be factored over real numbers\r\n" );
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document.write( "     =  -  =  -  = .\r\n" );
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document.write( "   +--------------------------------------------------------------------------------------------------------+\r\n" );
document.write( "   |  Far not everyone knows about this tricky decomposition; but those who are trained in Math, know it.   |\r\n" );
document.write( "   |      See the lesson  Advanced factoring  in this site.                                                 |\r\n" );
document.write( "   +--------------------------------------------------------------------------------------------------------+\r\n" );
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document.write( "Therefore, decomposition (1) can be continue farther\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "Three remaining quadratic polynomials CAN NOT be factored further over real numbers.\r\n" );
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document.write( "Therefore,  k = 5  is the largest value of \" k \"  under the problem's question.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The answer and the statement \" k = 4 \" by @greenestamps is not correct.\r
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