document.write( "Question 204627: Show that x-c is not a factor of f(x)=\"3x%5E4%2Bx%5E2%2B5\" for any real number c. \n" ); document.write( "
Algebra.Com's Answer #154445 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let's divide: \r\n" );
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document.write( "\"3x%5E4%2Bx%5E2%2B5\" by \"x-c\" using synthetic division:\r\n" );
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document.write( "We must express \"3x%5E4%2Bx%5E2%2B5\" as \"3x%5E4%2B0x%5E3%2Bx%5E2%2B0x%2B5\"\r\n" );
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document.write( " c | 3       0       1        0        5 \r\n" );
document.write( "   |        3c      3c2     c+3c3   c2+3c4\r\n" );
document.write( "    ----------------------------------------\r\n" );
document.write( "     3      3c    1+3c2     c+3c3  5+c2+3c4 \r\n" );
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document.write( "The remainder is 5+c2+3c4.  This is always\r\n" );
document.write( "a positive number because even powers of a\r\n" );
document.write( "real number are never negative. Thus this\r\n" );
document.write( "remainder can never be 0.\r\n" );
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document.write( "Edwin
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