document.write( "Question 1126946: Find a polynomial of the specified degree that satisfies the given conditions.
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Algebra.Com's Answer #743285 by Edwin McCravy(20063)\"\" \"About 
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Find a polynomial of the specified degree that satisfies the given conditions.
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document.write( "The zeros are:\r\n" );
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document.write( "Multiply left and right sides:\r\n" );
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document.write( "\"%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29+=+0\"\r\n" );
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document.write( "Multiply both sides by a constant A:\r\n" );
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document.write( "\"A%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29+=+0\"\r\n" );
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document.write( "FOIL out the last two parentheses on the left:\r\n" );
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document.write( "\"A%28x%2B3%29%28x%2B1%29%28x-3%29%28x%5E2-3%29+=+0\"\r\n" );
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document.write( "FOIL out the last two parentheses on the left again:\r\n" );
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document.write( "\"A%28x%2B3%29%28x%2B1%29%28x%5E3-3x-3x%5E2%2B9%29+=+0\"\r\n" );
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document.write( "Get the last parentheses in descending order:\r\n" );
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document.write( "\"A%28x%2B3%29%28x%2B1%29%28x%5E3-3x%5E2-3x%2B9%29+=+0\"\r\n" );
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document.write( "Multiply the last two factors in parentheses on the left:\r\n" );
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document.write( "\"A%28x%2B3%29%28x%5E4-2x%5E3-6x%5E2%2B6x%2B9%29=0\"\r\n" );
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document.write( "\"A%28x%5E5+%2B+x%5E4+-+12x%5E3+-+12x%5E2+%2B+27x+%2B+27%29=0\"\r\n" );
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document.write( "Distribute the A:\r\n" );
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document.write( "\"Ax%5E5+%2B+Ax%5E4+-+12Ax%5E3+-+12Ax%5E2+%2B+27Ax+%2B+27A%29=0\"\r\n" );
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document.write( "Since the constant term 27A must equal 54, we set\r\n" );
document.write( "them equal:\r\n" );
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document.write( "                    27A = 54\r\n" );
document.write( "                      A = 2\r\n" );
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document.write( "So \"Ax%5E5+%2B+Ax%5E4+-+12Ax%5E3+-+12Ax%5E2+%2B+27Ax+%2B+27A%29=0\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"2x%5E5+%2B+2x%5E4+-+12%282%29x%5E3+-+12%282%29x%5E2+%2B+27%282%29x+%2B+27%282%29%29=0\"\r\n" );
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document.write( " or\r\n" );
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document.write( "\"2x%5E5+%2B+2x%5E4+-+24x%5E3+-+24x%5E2+%2B+54x+%2B+54+=+0\"\r\n" );
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document.write( "So the polynomial is the left side without the \"= 0\".\r\n" );
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document.write( "\"2x%5E5+%2B+2x%5E4+-+24x%5E3+-+24x%5E2+%2B+54x+%2B+54\"\r\n" );
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document.write( "Edwin

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