document.write( "Question 983759: List all possible rational zeros of the polynomial function f(x)=2x^3-4x^2+5x+6. \n" ); document.write( "
Algebra.Com's Answer #604684 by Edwin McCravy(20056)\"\" \"About 
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2x^3-4x^2+5x+6
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document.write( "Given a polynomial with integer coefficients:\r\n" );
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document.write( "How to make a list of numbers such that if there are any rational zeros\r\n" );
document.write( "for a polynomial, they will all be in the list of numbers.\r\n" );
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document.write( "1.  Find all possible factors of the absolute value of the coefficient of the \r\n" );
document.write( "    nonzero term with LEAST degree. \r\n" );
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document.write( "2.  Find all possible factors of the absolute value of the coefficient of the \r\n" );
document.write( "    nonzero term with GREATEST degree. \r\n" );
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document.write( "3.  List all possible fractions whose numerator is in the first list and\r\n" );
document.write( "    whose denominator is in the second list.\r\n" );
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document.write( "4.  Also include all the negatives of those fractions.\r\n" );
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document.write( "1.  All the factor of 6 are 1,2,3,6\r\n" );
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document.write( "2.  All the factors of 2 are 1 and 2\r\n" );
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document.write( "3.  All the fractions are 1/1, 1/2, 2/1, 2/2, 3/1, 3/2, 6/1, 6/2\r\n" );
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document.write( "Reducting the reducible ones:\r\n" );
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document.write( "                            1, 1/2, 2, 1, 3, 3/2, 6, 3\r\n" );
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document.write( "Toss out the dupicates:     1, 1/2, 2, 3, 3/2, 6\r\n" );
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document.write( "4.  Also include their negatives (opposites:\r\n" );
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document.write( "                           ±1, ±1/2, ±2, ±3, ±3/2, ±6\r\n" );
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document.write( "If there are any rational zeros of 2x^3-4x^2+5x+6, they will be in\r\n" );
document.write( "that list.\r\n" );
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document.write( "As it turns out, unfortunately, none of those are zeros of  f(x)=2x^3-4x^2+5x+6.\r\n" );
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document.write( "[This proves that the word \"possible\", although all teachers and textbooks use\r\n" );
document.write( "that word, that is the wrong word to use because, for example, in this case none\r\n" );
document.write( "of them are really 'possible rational zeros'.]\r\n" );
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document.write( "Edwin
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