document.write( "Question 79499: When dividing the polynomials by synthetic division, what are the numbers we list across the top row in the division?
\n" ); document.write( "(2x^4-x^2+5x-7)/(x+4) \n" ); document.write( "
Algebra.Com's Answer #57049 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "When dividing the polynomials by synthetic division,\r\n" );
document.write( "what are the numbers we list across the top row in \r\n" );
document.write( "the division? \r\n" );
document.write( "\r\n" );
document.write( "\"%282x%5E4-x%5E2%2B5x-7%29%2F%28x%2B4%29\"\r\n" );
document.write( "\r\n" );
document.write( "You will notice there is a skip in the exponents of x\r\n" );
document.write( "in the top. That is, there is no term in x³ so we must\r\n" );
document.write( "insert the term +0x³:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\"%282x%5E4%2B0x%5E3-x%5E2%2B5x-7%29%2F%28x%2B4%29\"\r\n" );
document.write( "\r\n" );
document.write( "Then the top line of the synthetic division goes:\r\n" );
document.write( "\r\n" );
document.write( "        2  0 -1  5 -7 \r\n" );
document.write( "\r\n" );
document.write( "To do the synthetic division:\r\n" );
document.write( "\r\n" );
document.write( "     -4|2  0 -1    5  -7\r\n" );
document.write( "       |  -8 32 -124 476\r\n" );
document.write( "        2 -8 31 -119 469\r\n" );
document.write( "\r\n" );
document.write( "The division gives\r\n" );
document.write( "\r\n" );
document.write( "      \"2x%5E3-8x%5E2%2B31x-119%2B469%2F%28x%2B4%29\"\r\n" );
document.write( "\r\n" );
document.write( "and is a shortcut for this long division:\r\n" );
document.write( "\r\n" );
document.write( "               2x³ -  8x² +  31x - 119        \r\n" );
document.write( "   x + 4)2x4 + 0x³ -   x² +   5x -   7\r\n" );
document.write( "         2x4 + 8x³\r\n" );
document.write( "              -8x³ -   x²\r\n" );
document.write( "              -8x² - 32x²   \r\n" );
document.write( "                     31x² +   5x\r\n" );
document.write( "                     31x² + 124x\r\n" );
document.write( "                           -119x -   7\r\n" );
document.write( "                           -119x - 476 \r\n" );
document.write( "                                   469\r\n" );
document.write( "\r\n" );
document.write( "which gives the exact same answer, because if you will\r\n" );
document.write( "notice all the coefficients in the long division also \r\n" );
document.write( "occur as numbers in the synthetic division, except \r\n" );
document.write( "that the signs of the subtrahends in the long division\r\n" );
document.write( "are opposite because subtraction is done in the long \r\n" );
document.write( "divion whereas assition is done in the synthetic division.\r\n" );
document.write( "This conversion from subtraction to addition is \r\n" );
document.write( "accomplished by changing the sign of the 4 in the\r\n" );
document.write( "divisor x+4 to -4 in the synthetic division. \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );