document.write( "Question 472580: Find all zeros of the function and write the polynomial as a product of linear factors.\r
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\n" ); document.write( "\n" ); document.write( "A. \"+f%28x%29+=+%28x+-+4%29%28x+%2B+2%29%28x+-+3%29%28x+%2B+3%29+\"
\n" ); document.write( "B. \"+f%28x%29+=+%28x+%2B+4%29%28x+%2B+2%29%28x+-+3i%29%28x+%2B+3i%29+\"
\n" ); document.write( "C. \"+f%28x%29+=+%28x+-+1%29%28x+-+8%29%28x+-+3i%29%28x+%2B+3i%29+\"
\n" ); document.write( "D. \"+f%28x%29+=+%28x+-+i%28sqrt8%29%29%28x+%2B+i%28sqrt8%29%29%28x+-+3%29%28x+%2B3%29+\"
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Algebra.Com's Answer #323982 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If you know about DesCartes rule of signs, you don't have to do\r\n" );
document.write( "any work.  You will notice that there are no sign changes in \r\n" );
document.write( "going from the first term to the last.  Therefore it can have \r\n" );
document.write( "no positive zeros.  Only one of the choices has no positive \r\n" );
document.write( "zeros, so you don't have to do any work.\r\n" );
document.write( "Look at\r\n" );
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document.write( "B. \"+f%28x%29+=+%28x+%2B+4%29%28x+%2B+2%29%28x+-+3i%29%28x+%2B+3i%29+\"\r\n" );
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document.write( "and notice it's the only one that has no factors of the form \r\n" );
document.write( "\"x+-+A_POSITIVE_REAL_NUMBER\" like (x - 4) or (x - 3). \r\n" );
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document.write( "Setting each factor of B to zero gives:\r\n" );
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document.write( "x + 4 = 0        x + 2 = 0      x - 3i = 0       x + 3i = 0 \r\n" );
document.write( "    x = -4           x = -2          x = 3i           x = -3i\r\n" );
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document.write( "B is the only one that has only negative and imaginary zeros.\r\n" );
document.write( "The other answers have at least one negative zero which Descartes'\r\n" );
document.write( "rule of signs shows us. \r\n" );
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document.write( "[Setting any of the others choices to zero will give some negative \r\n" );
document.write( "zeros.  For instance if you set x - 4 = 0 you get a positive zero 4,\r\n" );
document.write( "and so you eliminate all that have a factor \"x - a positive number\" \r\n" );
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document.write( "Edwin
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