document.write( "Question 108209: Find the remainder when \"+2a%5E3-3a%5E2%2B4a%2B3+\" is synthetically divided by a+1/2. \n" ); document.write( "
Algebra.Com's Answer #78991 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Find the remainder when \"2a%5E3-3a%5E2%2B4a%2B3\" is synthetically divided by a + \"1%2F2\".\r\n" );
document.write( "
\r\n" );
document.write( "Change the sign of the \"1%2F2\" to \"-1%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |             \r\n" );
document.write( "                    \r\n" );
document.write( "Bring down the 2\r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |             \r\n" );
document.write( "    2             \r\n" );
document.write( "\r\n" );
document.write( "Multiply the 2 by the \"-1%2F2\" to get -1\r\n" );
document.write( "Write -1 above and to the right of the 2:\r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |   -1        \r\n" );
document.write( "    2             \r\n" );
document.write( "\r\n" );
document.write( "Combine the -3 and the -1, getting -4.\r\n" );
document.write( "Write -4 at the bottom beside the 2 \r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |    1        \r\n" );
document.write( "    2  -4   \r\n" );
document.write( "\r\n" );
document.write( "Multiply the -4 by the \"-1%2F2\" to get -2\r\n" );
document.write( "Write -2 above and to the right of the -4:\r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |    1  -2    \r\n" );
document.write( "    2  -4          \r\n" );
document.write( "\r\n" );
document.write( "Combine the 4 and the -2, getting 2.\r\n" );
document.write( "Write 2 at the bottom beside the -4: \r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |    1  -2    \r\n" );
document.write( "    2  -4   2   \r\n" );
document.write( "\r\n" );
document.write( "Multiply the 2 by the \"-1%2F2\" to get -1\r\n" );
document.write( "Write -1 above and to the right of the 2:\r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |    1  -2  -1\r\n" );
document.write( "    2  -4   2   \r\n" );
document.write( "\r\n" );
document.write( "Combine the 3 and the -1, getting 2.\r\n" );
document.write( "Write 2 at the bottom beside the 2: \r\n" );
document.write( "\r\n" );
document.write( "\"-1%2F2\"|2  -3   4   3\r\n" );
document.write( "   |    1  -2  -1\r\n" );
document.write( "    2  -4   2   2\r\n" );
document.write( "\r\n" );
document.write( "The synthetic division is now complete,\r\n" );
document.write( "and the remainder is the right-most term \r\n" );
document.write( "on the bottom line.  So the answer is 2.\r\n" );
document.write( "\r\n" );
document.write( "The quotient is gotten from the first three\r\n" );
document.write( "numbers on the bottom line and is interpreted\r\n" );
document.write( "as \r\n" );
document.write( "\r\n" );
document.write( "2x² - 4x + 2.\r\n" );
document.write( "\r\n" );
document.write( "But you were only asked to give the remainder\r\n" );
document.write( "which is the right-most number on the\r\n" );
document.write( "bottom line of the synthetic division. So\r\n" );
document.write( "the answer is 2.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
 \n" );
document.write( "
\n" );