document.write( "Question 1170859: find the values of A,B,C if (x-1),(x+2) and (x-2) are factor of
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Algebra.Com's Answer #795735 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "In accordance with the Remainder theorem,  the given part means that the given polynomial has the roots of 1, -2 and 2.\r\n" );
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document.write( "So we write these three equations expressing this fact\r\n" );
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document.write( "    2A*1^4    - B*1^3    - C*1     - 16 = 0\r\n" );
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document.write( "    2A*(-2)^4 - B*(-2)^3 - C*(-2)  - 16 = 0\r\n" );
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document.write( "    2A*2^4    - B*2^3    - C*2     - 16 = 0\r\n" );
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document.write( "or\r\n" );
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document.write( "    2A -  B -  C = 16    (1)\r\n" );
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document.write( "   32A + 8B + 2C = 16    (2)\r\n" );
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document.write( "   32A - 8B - 2C = 16    (3)\r\n" );
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document.write( "Adding equations (2) and (3), you get\r\n" );
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document.write( "   64A           = 32,   which implies  A =  = 0.5.\r\n" );
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document.write( "Then from (1) and (2), substituting A = 0.5 there, you get\r\n" );
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document.write( "     B +  C = -15        (4)\r\n" );
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document.write( "    8B + 2C =   0        (5)\r\n" );
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document.write( "Expressing  B = -15 - C  from (4)  and substituting it to (5), you get\r\n" );
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document.write( "    8*(-15 -C) + 2C = 0,    or\r\n" );
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document.write( "    -120 - 8C +  2C = 0\r\n" );
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document.write( "         - 6C = 120\r\n" );
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document.write( "            C = - 20.\r\n" );
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document.write( "Then from equation (4),  B = -15 - (-20) = -15 + 20 = 5.\r\n" );
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document.write( "ANSWER.  A = 0.5;  B = 5,  C = -20.\r\n" );
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