document.write( "Question 1083871: The expression 6y^2-y-51 can be rewritten as (3Ay+B)(y-C), where A, B, and C are positive integers. Find $
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Algebra.Com's Answer #697965 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "(3Ay + B)*(y - C) =  = .\r\n" );
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document.write( "Since it is identical to , we have\r\n" );
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document.write( "    3A = 6  and hence A = 2;             (1)\r\n" );
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document.write( "    B - 3AC = -1,   or  B - 6C = -1;     (2)\r\n" );
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document.write( "    BC = 51.                             (3)\r\n" );
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document.write( "Thus you actually have these two equations to determine B and C:\r\n" );
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document.write( "B - 6C = -1                              (2)\r\n" );
document.write( "BC = 51.                                 (3)\r\n" );
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document.write( "From (2), express B = 6C -1 and substitute it into (3). You will get\r\n" );
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document.write( "(6C-1)*C = 51.\r\n" );
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document.write( " = 0,\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "(C-3)*(2C+17) = 0.\r\n" );
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document.write( "Since you need C to be positive number (as the condition requires), you have only one possibility: C = 3.\r\n" );
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document.write( "Then B = 6C-1 = 6*3-1 = 17,\r\n" );
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document.write( "and now you have everything to calculate   =  =  = 19.\r\n" );
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