document.write( "Question 570933: how do i answer the question: list all possible rational zeros of each equation, with equations like x^3-7x+6=0? i have worked out the equation using synthetic division, but that takes too long, is there a faster way? \n" ); document.write( "
Algebra.Com's Answer #367882 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If you're only asked to list all POSSIBLE rational zeros,\r\n" );
document.write( "then they are NOT asking you to find the zeros. \r\n" );
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document.write( "They are merely asking you to list all the CANDIDATES for \r\n" );
document.write( "rational zeros.\r\n" );
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document.write( "It is unfortunate that all the algebra books use the word\r\n" );
document.write( "\"POSSIBLE\" and ask for all \"possible rational zeros\".  But \r\n" );
document.write( "they do!  They should say \"candidates for rational zeros\", \r\n" );
document.write( "because many times the candidates are not really \"possible\".\r\n" );
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document.write( "If a polynomial has rational zeros, then those rational zeros \r\n" );
document.write( "will be fractions of this form: \r\n" );
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document.write( "                \"%22%22+%2B-+%28factor_of_the_constant_term%29%2F%28factor_of_the_leading_coefficient%29\" \r\n" );
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document.write( "However, not all fractions of this form are necessarily zeros of the\r\n" );
document.write( "polynomial. Indeed it may happen that none of the fractions so formed\r\n" );
document.write( "are actually zeros of the polynomial.\r\n" );
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document.write( "Since the leading coefficient is 1, you need not worry about denominators\r\n" );
document.write( "in this polynomial.  All they want you to do is list all the positive and\r\n" );
document.write( "negative factors of the last term, 6, which are \r\n" );
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document.write( "                ±1, ±2, ±3, ±6\r\n" );
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document.write( "The only thing they are asking you to do is to list those!   \r\n" );
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document.write( "Since you have already found all the zeros, you know that they are\r\n" );
document.write( "-3, 1 and 2.  So you see that +3,-1,-2,+6, and -6 are not zeros at all.\r\n" );
document.write( "However they were CANDIDATES for aeros and so you should list all\r\n" );
document.write( "the candidates for solutions.  \r\n" );
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document.write( "I think you were misled, and understandably so, by the word \"POSSIBLE\".\r\n" );
document.write( "I wish they would use another word.\r\n" );
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document.write( "Edwin
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