document.write( "Question 1030211: If \"%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+n\"
\n" ); document.write( "for integers a, b, m and n, what is the product of m and n? \n" ); document.write( "
Algebra.Com's Answer #645101 by Edwin McCravy(20060)\"\" \"About 
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If \"%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+n\"
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document.write( "Since this true for all x,\r\n" );
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document.write( "\"%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+n\"\r\n" );
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document.write( "then it's true when x=0\r\n" );
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document.write( "\"6b=n\".  Substitute 6b for n\r\n" );
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document.write( "\"%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+6b\"\r\n" );
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document.write( "It's also true when x=1:\r\n" );
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document.write( "\"10%281%2Ba%2Bb%29=1%2Bm%2B6b\"\r\n" );
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document.write( "\"10%2B10a%2B10b=1%2Bm%2B6b\"\r\n" );
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document.write( "\"10a%2B4b-m=-9\"\r\n" );
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document.write( "It's also true when x=-1:\r\n" );
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document.write( "\"4%281-a%2Bb%29=1%2Bm%2B6b\"\r\n" );
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document.write( "\"4-4a%2B4b=1%2Bm%2B6b\"\r\n" );
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document.write( "\"-4a-2b-m=-3\"\r\n" );
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document.write( "Multiply through by -1:\r\n" );
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document.write( "\"4a%2B2b%2Bm=3\"\r\n" );
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document.write( "It's also true when x=2:\r\n" );
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document.write( "\"16%284%2B2a%2Bb%29=16%2B4m%2B6b\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"8%284%2B2a%2Bb%29=8%2B2m%2B3b\"\r\n" );
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document.write( "\"32%2B16a%2B8b=8%2B2m%2B3b\"\r\n" );
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document.write( "\"16a%2B5b-2m=-24\"\r\n" );
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document.write( "Solve the system:\r\n" );
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document.write( "\"10a%2B4b-m=-9\"\r\n" );
document.write( "\"4a%2B2b%2Bm=3\"\r\n" );
document.write( "\"16a%2B5b-2m=-24\"\r\n" );
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document.write( "Then take the value for b, substitute it in \"6b=n\"\r\n" );
document.write( "to find n.  Take the value for m, multiply it by\r\n" );
document.write( "the value you get for n and get mn.  You finish.\r\n" );
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document.write( "Edwin
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