document.write( "Question 631640: I thought I understood this, but I'm completely lost. Can you please help me to understand it?\r
\n" ); document.write( "\n" ); document.write( "(t4 − 2t2 + 4t − 5) ÷ (t2 − 3) \n" ); document.write( "
Algebra.Com's Answer #397773 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "(t4 − 2t² + 4t − 5) ÷ (t² − 3)\r\n" );
document.write( "\r\n" );
document.write( "Put in terms with 0 coefficients for place holders:\r\n" );
document.write( "\r\n" );
document.write( "(t4 + 0t³ - 2t² + 4t - 5) ÷ (t² + 0t - 3)\r\n" );
document.write( "\r\n" );
document.write( "           ________________________\r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "\r\n" );
document.write( "Divide t4 ÷ t² = t² so put that above the line above the - 3t²\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                        t²             \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "\r\n" );
document.write( "Multiply the t² times the t² + 0t - 3, t²(t² + 0t - 3) = t4 + 9t³ - 3t² \r\n" );
document.write( "and put that under the corresponding terms and draw a line underneath:\r\n" );
document.write( "\r\n" );
document.write( "                        t²         \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "            \r\n" );
document.write( "Now subtract (t4 + 0t³ - 2t²) - (t4 + 0t³ - 3t²) = \r\n" );
document.write( "t4 + 0t³ - 2t² - t4 - 0t³ + 3t² = 0t³ + t². Put that below the line and \r\n" );
document.write( "bring down the next term + 4t:\r\n" );
document.write( "\r\n" );
document.write( "                        t²        \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "\r\n" );
document.write( "Divide 0t³ ÷ t² = 0t so put that above the line above the + 4t\r\n" );
document.write( " \r\n" );
document.write( "                        t² + 0t    \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "\r\n" );
document.write( "Multiply the 0t times the t² + 0t - 3, 0t(t² + 0t - 3) = 0t³ + 0t² + 0t\r\n" );
document.write( "and put that under the corresponding terms and draw a line underneath:\r\n" );
document.write( "\r\n" );
document.write( "                        t² + 0t    \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "                 0t³ + 0t² + 0t\r\n" );
document.write( "\r\n" );
document.write( "Now subtract (0t³ +  t² + 4t) - (0t³ + 0t³ - 3t²) = \r\n" );
document.write( "0t³ +  t³ + 4t - 0t³ + 0t² + 0t = t³ + 4t. Put that below the \r\n" );
document.write( "line and bring down the next (last) term - 5:\r\n" );
document.write( "\r\n" );
document.write( "                        t² + 0t    \r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "                 0t³ + 0t² + 0t\r\n" );
document.write( "                        t² + 4t - 5\r\n" );
document.write( "\r\n" );
document.write( "Divide t² ÷ t² = 1 so put that above the line above the - 5\r\n" );
document.write( "\r\n" );
document.write( "                        t² + 0t + 1\r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "                 0t³ + 0t² + 0t\r\n" );
document.write( "                        t² + 4t - 5\r\n" );
document.write( "\r\n" );
document.write( "Multiply the 1 times the t² + 0t - 3, 1(t² + 0t - 3) =  t³ + 0t - 3 \r\n" );
document.write( "and put that under the corresponding terms and draw a line underneath:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                        t² + 0t + 1\r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "                 0t³ + 0t² + 0t\r\n" );
document.write( "                        t² + 4t - 5\r\n" );
document.write( "                        t³ + 0t - 3\r\n" );
document.write( "\r\n" );
document.write( "Now subtract (t² + 4t - 5) - (t² + 0t - 3) = \r\n" );
document.write( "              t² + 4t - 5 - t² - 0t² + 3 =  \r\n" );
document.write( "              4t - 2. Put that below the line\r\n" );
document.write( "\r\n" );
document.write( "                        t² + 0t + 1\r\n" );
document.write( "t² + 0t - 3)t4 + 0t³ - 2t² + 4t - 5\r\n" );
document.write( "            t4 + 0t³ - 3t²\r\n" );
document.write( "                 0t³ +  t² + 4t\r\n" );
document.write( "                 0t³ + 0t² + 0t\r\n" );
document.write( "                        t² + 4t - 5\r\n" );
document.write( "                        t³ + 0t - 3\r\n" );
document.write( "                             4t - 2\r\n" );
document.write( "\r\n" );
document.write( "There are no more terms to bring down, so we are done with\r\n" );
document.write( "the dividion, and are ready to write the answer:\r\n" );
document.write( "\r\n" );
document.write( "We use the formula Answer = QUOTIENT + \"REMAINDER%2FDIVISOR\"\r\n" );
document.write( "\r\n" );
document.write( "                   t² + 0t + 1 + \"%284t-2%29%2F%28t%5E2%2B0t-3%29\"\r\n" );
document.write( "\r\n" );
document.write( " Now we can drop the 0 terms:\r\n" );
document.write( "\r\n" );
document.write( "                   t² + 1 + \"%284t-2%29%2F%28t%5E2-3%29\" \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );