document.write( "Question 936321: What polynomial of minimum degree fits the data?\r
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Algebra.Com's Answer #569752 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are 4 points,\r\n" );
document.write( "(-2,61)  (2,-21)  (3,4)  (5,240)\r\n" );
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document.write( "so we need a polynomial that has 4 \r\n" );
document.write( "unknown coefficients,   \r\n" );
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document.write( "\"y=Ax%5E3%2BB%5Ex%5E2%2BCx%2BD\"\r\n" );
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document.write( "so we can substitute each of those \r\n" );
document.write( "4 points in it:\r\n" );
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document.write( "\"-61=A%28-2%29%5E3%2BB%28-2%29%5E2%2BC%28-2%29%2BD\"\r\n" );
document.write( "\"-21=A%282%29%5E3%2BB%282%29%5E2%2BC%282%29%2BD\"\r\n" );
document.write( "\"4=A%283%29%5E3%2BB%283%29%5E2%2BC%283%29%2BD\"\r\n" );
document.write( "\"240=A%285%29%5E3%2BB%285%29%5E2%2BC%285%29%2BD\"\r\n" );
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document.write( "Simplifying each:\r\n" );
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document.write( "\"-61=A%28-8%29%2BB%284%29-2C%2BD\"\r\n" );
document.write( "\"-21=A%288%29%2BB%284%29%2B2C%2BD\"\r\n" );
document.write( "\"4=A%2827%29%2BB%289%29%2B3C%2BD\"\r\n" );
document.write( "\"240=A%28125%29%2BB%2825%29%2B5C%2BD\"\r\n" );
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document.write( "Simplifying further:\r\n" );
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document.write( "\"-61=-8A%2B4B-2C%2BD\"\r\n" );
document.write( "\"-21=8A%2B4B%2B2C%2BD\"\r\n" );
document.write( "\"4=27A%2B9B%2B3C%2BD\"\r\n" );
document.write( "\"240=125A%2B25B%2B5C%2BD\"\r\n" );
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document.write( "Put the constants on tyhe right\r\n" );
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document.write( "Solve that system and get A=4, B=-9, C=-6, D=-5\r\n" );
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document.write( "If you have trouble solving that system, post again.\r\n" );
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document.write( "So\r\n" );
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document.write( "\"y=Ax%5E3%2BB%5Ex%5E2%2BCx%2BD\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"y=4x%5E3-9x%5E2-6x-5\"\r\n" );
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document.write( "Edwin

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