document.write( "Question 427656: please explain how to do long division
\n" ); document.write( "(b^3-27)/(b-3)=
\n" ); document.write( "and then how do I check this \n" ); document.write( "
Algebra.Com's Answer #297414 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
(b³-27)/(b-3)=
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document.write( "Write b³ - 27 as b³ + 0b² + 0b - 27 \r\n" );
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document.write( "Write this:\r\n" );
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document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      \r\n" );
document.write( "b³ divided by b give b²\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "     \r\n" );
document.write( "b² times -3 gives -3b\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "         - 3b²\r\n" );
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document.write( "b² times b gives b³\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
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document.write( "Draw a line:\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
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document.write( "Subtract b³ - b³, that gives 0 so we don't write anything\r\n" );
document.write( "under that.  then 0b² minus -3b² is really 0b²+3b² or 3b²\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b²\r\n" );
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document.write( "Bring down the + 0b\r\n" );
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document.write( "            b²          \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
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document.write( "3b² divided by b give 3b\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
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document.write( "3b times -3 gives -9b\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "               - 9b\r\n" );
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document.write( "3b times b gives 3b²\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "\r\n" );
document.write( "Draw a line:\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
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document.write( "Subtract 3b² - 3b², that gives 0 so we don't write anything\r\n" );
document.write( "under that.  then 0b minus -9b is really 0b+9b or 9b\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b\r\n" );
document.write( "\r\n" );
document.write( "Bring down the - 27\r\n" );
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document.write( "            b² + 3b     \r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
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document.write( "9b divided by b give 9\r\n" );
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document.write( "            b² + 3b + 9\r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
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document.write( "9 times -3 gives -27\r\n" );
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document.write( "            b² + 3b + 9\r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
document.write( "                    - 27\r\n" );
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document.write( "9 times b gives 9b\r\n" );
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document.write( "            b² + 3b + 9\r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
document.write( "                 9b - 27\r\n" );
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document.write( "Draw a line:\r\n" );
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document.write( "            b² + 3b + 9\r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
document.write( "                 9b - 27\r\n" );
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document.write( "Subtract 9b - 9b, that gives 0 so we don't write anything\r\n" );
document.write( "under that.  then -27 minus -27 is really -27+27 or 0, so\r\n" );
document.write( "the remainder is 0:\r\n" );
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document.write( "            b² + 3b + 9\r\n" );
document.write( "b - 3)b³ + 0b² + 0b - 27\r\n" );
document.write( "      b³ - 3b²\r\n" );
document.write( "           3b² + 0b\r\n" );
document.write( "           3b² - 9b\r\n" );
document.write( "                 9b - 27\r\n" );
document.write( "                 9b - 27\r\n" );
document.write( "                       0\r\n" );
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document.write( "That's it.  The answer, or quotient, is b² + 3b + 9\r\n" );
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document.write( "Edwin
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