document.write( "Question 242898: Please show me how to divide by long division this: (3x^3+4x-1) / (x^2+1) \n" ); document.write( "
Algebra.Com's Answer #177879 by Edwin McCravy(20059) $\"\"$ $\"About$
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document.write( "You have to put in placeholder zeros for the missing powers in both the \r\n" );
document.write( "divisor and the dividend, and deal with 0 placeholders all through\r\n" );
document.write( "the long division process.\r\n" );
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document.write( "You have to write  as  and\r\n" );
document.write( "you have to write  as \r\n" );
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document.write( "Then you write this:\r\n" );
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document.write( "         \r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1 \r\n" );
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document.write( "Divide  getting  and write this\r\n" );
document.write( "above the line in line with the 4x:\r\n" );
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document.write( "                        3x\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1 \r\n" );
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document.write( "Now multiply 3x by x² + 0x + 1, getting 3x³ + 0x² + 3x,\r\n" );
document.write( "and write it below like this, keeping like powers of x\r\n" );
document.write( "lined up, then draw a line underneath.\r\n" );
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document.write( "                        3x\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                   \r\n" );
document.write( "Now subtract (3x³ + 0x² + 4x) - (3x³ + 0x² + 3x) = 0x² + x.\r\n" );
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document.write( "(Not you must keep the placeholder zero for the x² term:\r\n" );
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document.write( "                        3x\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                  0x² +  x\r\n" );
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document.write( "Now bring down the next (last) term -1:\r\n" );
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document.write( "                        3x\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                  0x² +  x - 1\r\n" );
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document.write( "Next divide  getting 0, so write + 0\r\n" );
document.write( "on top above the -1:\r\n" );
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document.write( "                        3x + 0\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                  0x² +  x - 1\r\n" );
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document.write( "Multiply 0 by x² + 0x + 1 getting 0x² + 0x + 0 and\r\n" );
document.write( "write it at the bottom. Then draw a line:\r\n" );
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document.write( "                        3x + 0\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                  0x² +  x - 1\r\n" );
document.write( "                  0x² + 0x + 0\r\n" );
document.write( "                  ------------\r\n" );
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document.write( "Subtract: (0x² +  x - 1) - (0x² + 0x + 0) = x - 1, so\r\n" );
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document.write( "write that at the bottom:\r\n" );
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document.write( "                        3x + 0\r\n" );
document.write( "           ------------------- \r\n" );
document.write( "x² + 0x + 1)3x³ + 0x² + 4x - 1\r\n" );
document.write( "            3x³ + 0x² + 3x\r\n" );
document.write( "            --------------\r\n" );
document.write( "                  0x² +  x - 1\r\n" );
document.write( "                  0x² + 0x + 0\r\n" );
document.write( "                  ------------\r\n" );
document.write( "                         x - 1\r\n" );
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document.write( "Now the final answer is gotten by adding the fraction\r\n" );
document.write( " to the quotient:\r\n" );
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document.write( "Now we can drop the place holder zeros and get:\r\n" );
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document.write( "Edwin
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