document.write( "Question 1057542: write a polynomial function of the least degree that has rational coefficients, a leading coefficient of 1 and the given zeros. zeros are 3 and 1-square root of 3.\r
\n" ); document.write( "\n" ); document.write( "f(x) = (x-3)*(x-1-sqr root3)*(x-1+sq rt 3)\r
\n" ); document.write( "\n" ); document.write( "not sure how to proceed from here
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Algebra.Com's Answer #677272 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
\"%22f%28x%29%22\"\"%22%22=%22%22\"\"%28x%5E%22%22-3%29%28x%5E%22%22-1-sqrt%283%29%29%2A%28x%5E%22%22-1%2Bsqrt%283%29%29\"
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document.write( "Start by putting in some inner parentheses in the last two factors:\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "Now multiply the last two parentheses using FOIL.  When you do,\r\n" );
document.write( "the \"Inner\" and \"Outer\" terms will cancel out: \r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"%28x%5E%22%22-3%29%28%28x-1%29%5E2%2Bsqrt%283%29%28x-1%29-sqrt%283%29%28x-1%29-3%29\"\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "In fact we could have skipped that and gone straight to:\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"%28x%5E%22%22-3%29%28%28x-1%29%5E2-3%29\"\r\n" );
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document.write( "Now use FOIL again:\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"x%28x-1%29%5E2-3x-3%28x-1%29%5E2%2B9%29\"\r\n" );
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document.write( "Now simplify \"%28x-1%29%5E2=%28x-1%29%28x-1%29=x%5E2-x-x%2B1=x%5E2-2x%2B1\" <--FOIL again!\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"x%28x%5E2-2x%2B1%29-3x-3%28x%5E2-2x%2B1%29%2B9%29\"\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"x%5E3-2x%5E2%2Bx-3x-3x%5E2%2B6x-3%2B9%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"x%5E3+-+5x%5E2+%2B+4x+%2B+6\"\r\n" );
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document.write( "Edwin
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