\r\n" );
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document.write( "The other method is fine if you have memorized the binomial expansion\r\n" );
document.write( "identity:\r\n" );
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document.write( "(x + y)³ = x³ + 3x²y + 3xy² + y³\r\n" );
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document.write( "and observe how close it is to the given cubic polynomial. But most\r\n" );
document.write( "students probably haven't memorized this. So I did it the other way:\r\n" );
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document.write( "
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document.write( "We search for rational roots which are ± factors of 2,\r\n" );
document.write( "which are ±1, ±2\r\n" );
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document.write( "There are no sign changes so there are no positive roots,\r\n" );
document.write( "So the only rational roots, if any, are -1 and -2\r\n" );
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document.write( "We try -1\r\n" );
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document.write( "-1 | 1 3 3 2\r\n" );
document.write( " | -1 -2 -1 \r\n" );
document.write( " 1 2 1 1\r\n" );
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document.write( "No, for the remainder is not 0.\r\n" );
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document.write( "We try -1\r\n" );
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document.write( "-2 | 1 3 3 2\r\n" );
document.write( " | -2 -2 -2 \r\n" );
document.write( " 1 1 1 0\r\n" );
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document.write( "Yes, for the remainder is 0.\r\n" );
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document.write( "We divided by a+2 and the quotient is determined by\r\n" );
document.write( "the first three numbers on the bottom of the synthetic\r\n" );
document.write( "division. The quotient is 1a² + 1a + 1 or a² + a + 1.\r\n" );
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document.write( "(a + 2)(a² + a + 1) <--answer\r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
