document.write( "Question 1200950: If the polynomial function
\n" ); document.write( "P(x) = an^x^n + an−1^x^n−1 + ... + a1^x + a0
\n" ); document.write( "has integer coefficients, then the only numbers that could possibly be rational
\n" ); document.write( "zeros of P are all of the form p/q, where p is a factor of the constant coefficient a0 and q is a factor of the leading coefficient an
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\n" ); document.write( "The possible rational zeros of P(x) = 10x^3 + 6x^2 − 21x − 34 are:
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Algebra.Com's Answer #835175 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "If the polynomial function P(x) = an^x^n + an−1^x^n−1 + ... + a1^x + a0
\n" ); document.write( "has integer coefficients, then the only numbers that could possibly be rational zeros of P
\n" ); document.write( "are all of the form p/q, where p is a factor of the constant coefficient a0
\n" ); document.write( "and q is a factor of the leading coefficient an\r
\n" ); document.write( "\n" ); document.write( "The possible rational zeros of P(x) = 10x^3 + 6x^2 − 21x − 34 are:
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\n" ); document.write( "\n" ); document.write( " In this problem, they do not ask you to find the zeros.\r
\n" ); document.write( "\n" ); document.write( " They want you form the list of $\"highlight%28possible%29\"$ rational zeroes, based on the described algorithm.\r
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document.write( "So, based on the described algorithm, you write the list of all integer factors of \r\n" );
document.write( "the constant term p= a0 = -34.  These factors are\r\n" );
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document.write( "    +/- 1, +/- 2, +/- 17, +/- 34.\r\n" );
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document.write( "Next, you write the list of all factors of the leading coefficients q= an = 10.\r\n" );
document.write( "These factors are\r\n" );
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document.write( "    +/- 1, +/- 2, +/- 5, +/- 10.\r\n" );
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document.write( "Now the list of all possible rational zeroes ( the list of all   ) \r\n" );
document.write( "is the long set of all possible ratios\r\n" );
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document.write( "   { +/- 1,    +/- 2,    +/- 17,   +/- 34,\r\n" );
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document.write( "     +/- 1/2,  +/- 2/2,  +/-17/2,  +/- 34/2,\r\n" );
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document.write( "     +/- 1/5,  +/- 2/5,  +/-17/5,  +/- 34/5,\r\n" );
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document.write( "     +/- 1/10, +/- 2/10, +/-17/10, +/- 34/10 }.\r\n" );
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document.write( "The last step is to reduce / (to simplify) the fractions - where it is possible, \r\n" );
document.write( "and remove the repeating terms, that can arise after reducing. \r\n" );
document.write( "So, the final list is this\r\n" );
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document.write( "   { +/- 1,    +/- 2,    +/- 17,    +/- 34,\r\n" );
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document.write( "     +/- 1/2,            +/- 17/2,  \r\n" );
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document.write( "     +/- 1/5,  +/- 2/5,  +/- 17/5,  +/- 34/5,\r\n" );
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document.write( "     +/- 1/10,           +/- 17/10           }.\r\n" );
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