document.write( "Question 148086: Divide using long division: 6x^3 + 19x^2 + x - 10 / 2x - 1 \n" ); document.write( "
Algebra.Com's Answer #108485 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
$\"%286x%5E3+%2B+19x%5E2+%2B+x+-+10%29%2F%282x+-+1%29\"$
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document.write( "Start with this:\r\n" );
document.write( "              \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        \r\n" );
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document.write( "2x divides into 6x³ to give 3x²\r\n" );
document.write( "Put that at the top, above the 19x²  \r\n" );
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document.write( "               3x²       \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "      \r\n" );
document.write( "Multiply the 3x² by the 2x - 1 to get 6x³ - 3x²,\r\n" );
document.write( "so write that at the bottom and draw a line:\r\n" );
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document.write( "               3x² \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "           \r\n" );
document.write( "Now subtract, by mentally changing the signs on\r\n" );
document.write( "the bottom row.  We get 22x², so we write that\r\n" );
document.write( "at the bottom, and bring down the next term x:\r\n" );
document.write( "\r\n" );
document.write( "                       \r\n" );
document.write( "               3x² \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              \r\n" );
document.write( "2x divides into 22x² to give 11x\r\n" );
document.write( "Put that at the top above the x \r\n" );
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document.write( "               3x² + 11x \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "                 \r\n" );
document.write( "Multiply the 11x by the 2x - 1 to get 22x² - 11x,\r\n" );
document.write( "so write that at the bottom and draw a line:\r\n" );
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document.write( "               3x² + 11x +  6\r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              22x² - 11x\r\n" );
document.write( "              ----------\r\n" );
document.write( "\r\n" );
document.write( "Now subtract, by mentally changing the signs on\r\n" );
document.write( "the bottom row.  We get 12x, so we write that\r\n" );
document.write( "at the bottom, and bring down the next term -10:\r\n" );
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document.write( "\r\n" );
document.write( "               3x² + 11x \r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              22x² - 11x\r\n" );
document.write( "              ----------\r\n" );
document.write( "                     12x - 10\r\n" );
document.write( "       \r\n" );
document.write( "2x divides into 12x to give 6\r\n" );
document.write( "Put that at the top above the -10 \r\n" );
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document.write( "\r\n" );
document.write( "               3x² + 11x +  6\r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              22x² - 11x\r\n" );
document.write( "              ----------\r\n" );
document.write( "                     12x - 10\r\n" );
document.write( "                    \r\n" );
document.write( "Multiply the 6 by the 2x - 1 to get 12x - 6,\r\n" );
document.write( "so write that at the bottom and draw a line:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "               3x² + 11x +  6\r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              22x² - 11x\r\n" );
document.write( "              ----------\r\n" );
document.write( "                     12x - 10\r\n" );
document.write( "                     12x -  6\r\n" );
document.write( "                     --------\r\n" );
document.write( "                         \r\n" );
document.write( "Now subtract, by mentally changing the signs on\r\n" );
document.write( "the bottom row.  We get -4, so we write that\r\n" );
document.write( "at the bottom, and we're finished because there\r\n" );
document.write( "are no more terms to bring down:\r\n" );
document.write( "\r\n" );
document.write( "               3x² + 11x +  6\r\n" );
document.write( "       ---------------------- \r\n" );
document.write( "2x - 1 )6x³ + 19x² +   x - 10\r\n" );
document.write( "        6x³ -  3x²\r\n" );
document.write( "        ----------\r\n" );
document.write( "              22x² +   x\r\n" );
document.write( "              22x² - 11x\r\n" );
document.write( "              ----------\r\n" );
document.write( "                     12x - 10\r\n" );
document.write( "                     12x -  6\r\n" );
document.write( "                     --------\r\n" );
document.write( "                         -  4\r\n" );
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document.write( "Now we write the answer using\r\n" );
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document.write( "   \r\n" );
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document.write( "   \r\n" );
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document.write( "or if you like:\r\n" );
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document.write( "   \r\n" );
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document.write( "Edwin
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