document.write( "Question 697677: What is the binomial factor of p^4-6p^3+7p^2+7p-3 \n" ); document.write( "
Algebra.Com's Answer #430206 by Edwin McCravy(20056)\"\" \"About 
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document.write( "p4 - 6p³ + 7p² + 7p - 3\r\n" );
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document.write( "If there are any rational zeros (roots) they must be ± a factor of \r\n" );
document.write( "the absolute value of the contant term, |-3| or 3\r\n" );
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document.write( "All candidates for roots are 1,-1,3,-3\r\n" );
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document.write( "We try 1, using synthetic division:\r\n" );
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document.write( "1|1 -6  7  7 -3\r\n" );
document.write( " |   1 -5  2  9\r\n" );
document.write( "  1 -5  2  9  6\r\n" );
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document.write( "No, 1 is not a zero (root) for that remainder \r\n" );
document.write( "is 6, not 0\r\n" );
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document.write( "We try -1\r\n" );
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document.write( "-1|1 -6  7   7 -3\r\n" );
document.write( "  |  -1  7 -14  7\r\n" );
document.write( "   1 -7 14  -7  4\r\n" );
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document.write( "No, -1 is not a zero (root) for that remainder \r\n" );
document.write( "is 4, not 0\r\n" );
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document.write( "We try 3\r\n" );
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document.write( "3|1 -6  7  7 -3\r\n" );
document.write( " |   3 -9 -6  3\r\n" );
document.write( "  1 -3 -2  1  0\r\n" );
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document.write( "Yes, 3 is a zero (root) for that remainder \r\n" );
document.write( "is 0.  And the numbers across the bottom except\r\n" );
document.write( "for the last one, the 0, are the coefficients\r\n" );
document.write( "of the quotient,  So we have factored\r\n" );
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document.write( "p4 - 6p³ + 7p² + 7p - 3  as\r\n" );
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document.write( "(p - 3)(p³ - 3p² - 2p + 1)\r\n" );
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document.write( "So the binomial factor is p - 3.\r\n" );
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document.write( "Edwin
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