document.write( "Question 639899: if f(x)= ax˛ + bx + c is divided by x+2, x-1, and x-3, it leaves a remainder of 64, 1, and 22, respectively.\r
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Algebra.Com's Answer #402921 by Edwin McCravy(20055)\"\" \"About 
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\n" ); document.write( "if f(x)= ax˛ + bx + c is divided by x+2, x-1, and x-3, it leaves a remainder of 64, 1, and 22, respectively.\r
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document.write( "The remainder theorem tells us that if we divide a polynomial f(x) by\r\n" );
document.write( "x-a, the remainder will be f(a).\r\n" );
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document.write( "Therefore:\r\n" );
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document.write( "The remainder theorem tells us that if we divide f(x) = ax˛ + bx + c by\r\n" );
document.write( "x+2, the remainder will be f(-2), which is a(-2)˛+b(-2)+c or 4a-2b+c and\r\n" );
document.write( "since that's given to be 64 we have the equation:\r\n" );
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document.write( "4a-2b+c = 64\r\n" );
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document.write( "The remainder theorem tells us that if we divide f(x) = ax˛ + bx + c by\r\n" );
document.write( "x-1, the remainder will be f(1), which is a(1)˛+b(1)+c or a+b+c and\r\n" );
document.write( "since that's given to be 1 we have the equation:\r\n" );
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document.write( "a+b+c = 1\r\n" );
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document.write( "The remainder theorem tells us that if we divide f(x) = ax˛ + bx + c by\r\n" );
document.write( "x-3, the remainder will be f(3), which is a(3)˛+b(3)+c or 9a+3b+c and\r\n" );
document.write( "since that's given to be 22 we have the equation:\r\n" );
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document.write( "9a+3b+c = 22\r\n" );
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document.write( "So we have the system of three equations:\r\n" );
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document.write( "4a-2b+c = 64\r\n" );
document.write( " a+ b+c =  1\r\n" );
document.write( "9a+3b+c = 22\r\n" );
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document.write( "Solve that system and get a=\"63%2F10\", b=\"-147%2F10\" and c=\"47%2F5\"\r\n" );
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document.write( "Those are terrible fractions, but they are correct.\r\n" );
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document.write( "Edwin

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