document.write( "Question 394181: Carry out the following divisions and also write each in the form P(x)=D(x)Q(x)+R(x):\r
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Algebra.Com's Answer #279676 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "P(x) = x² - x + 1 = original Polynomial\r\n" );
document.write( "D(x) = x² + x + 1 = Divisor polynomial\r\n" );
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document.write( "So we divide the original Polynomial P(x) \r\n" );
document.write( "by the Divisor polynomial D(x) to find the\r\n" );
document.write( "Quotient polynomial Q(x) and the Remainder\r\n" );
document.write( "polynomial R(x). \r\n" );
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document.write( "Here is the outline of the division you are\r\n" );
document.write( "to do:\r\n" );
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document.write( "      Q(x)\r\n" );
document.write( "D(x) )P(x) \r\n" );
document.write( "      ....\r\n" );
document.write( "      R(x)    \r\n" );
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document.write( "So here is the division:\r\n" );
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document.write( "                      1\r\n" );
document.write( "x² + x + 1)x² - x + 1\r\n" );
document.write( "            x² + x + 1\r\n" );
document.write( "                -2x + 0\r\n" );
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document.write( "So the quotient polynomial Q(x) is simply 1,\r\n" );
document.write( "and the Remainder polynomial R(x) is -2x, so\r\n" );
document.write( "putting it in the form P(x)=D(x)Q(x)+R(x),\r\n" );
document.write( "we have:\r\n" );
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document.write( "     P(x)    =      D(x)  *  Q(x) + R(x)  \r\n" );
document.write( "       |             |        |      | \r\n" );
document.write( "(x² - x + 1) = (x² + x + 1)(1) + (-2x)\r\n" );
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document.write( "Edwin
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