document.write( "Question 1031087: I've had a go at this sequence of questions and come up with some answers, the thing is, I'm not sure that it's correct, please have a look and advise me if you have the time.
\n" ); document.write( "Problem(s); \r
\n" ); document.write( "\n" ); document.write( "i Determine the remainder when 9 x^5-4 x^4 is divided by 3 x-1\r
\n" ); document.write( "\n" ); document.write( "ii Show using the factor theorem the 2x -1 is a factor of 2x^4- x3 -6x^2 + 5x -1 and hence express \r
\n" ); document.write( "\n" ); document.write( "2x^4- x3 -6x^2 + 5x -1 as a product of a linear and cubic factor.\r
\n" ); document.write( "\n" ); document.write( "this is my go at the first bit:\r
\n" ); document.write( "\n" ); document.write( " 9 x^5-4 x^4 = (3 x^4-x^3/3-x^2/9-x/27-1/81) × (3 x-1)+-1/81 \n" ); document.write( "

Algebra.Com's Answer #645783 by josgarithmetic(39630) $\"\"$ $\"About$

You can put this solution on YOUR website!
(i)\r
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\n" ); document.write( "\n" ); document.write( "Do some factoring of the dividend first.
\n" ); document.write( " $\"9x%5E5-4x%5E4\"$
\n" ); document.write( " $\"x%5E4%289x-4%29\"$ ------but do you want to go this way, or do you want to entire dividend including the degrees of x with coefficients of 0?\r
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\n" ); document.write( "\n" ); document.write( "Here is the polynomial division using divisor $\"3x-1\"$ .
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document.write( "              3x^4    -(x^3)/3  -(1/9)x^2          -(1/27)x     (1/72)\r\n" );
document.write( "        _________________________________________________________________________\r\n" );
document.write( "3x-1    |     9x^5    -4x^4    0x^3                   0x^2       0x       \r\n" );
document.write( "        | \r\n" );
document.write( "        |     9x^5    -3x^4\r\n" );
document.write( "          -------------------\r\n" );
document.write( "              0       -x^4     0x^3\r\n" );
document.write( "                      -x^4     x^3/3\r\n" );
document.write( "                    -----------------\r\n" );
document.write( "                       0    -(1/3)x^3  0x^2\r\n" );
document.write( "                            -(1/3)x^3  (1/9)x^2\r\n" );
document.write( "                          ----------------------\r\n" );
document.write( "                               0      -(1/9)x^2   0x\r\n" );
document.write( "                                      -(1/9)x^2  -(1/27)x\r\n" );
document.write( "                                     --------------------\r\n" );
document.write( "                                        0       (1/27)x         0\r\n" );
document.write( "                                                (1/27)x      -(1/72)\r\n" );
document.write( "                                               ---------------------\r\n" );
document.write( "                                                  0         (1/72)\r\n" );
document.write( "                                     \r\n" );
document.write( "\r\n" );
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document.write( "

\n" ); document.write( "According to that polynomial long division, the quotient INCLUDING remainder is $\"1%2F72\"$ and the quotient including the meaning for the remainder is
\n" ); document.write( " $\"3x%5E4-%281%2F3%29x%5E3-%281%2F9%29x%5E2-%281%2F27%29x%2B1%2F%2872%283x-1%29%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"3x%5E4-%281%2F3%29x%5E3-%281%2F9%29x%5E2-%281%2F27%29x%2B1%2F%28216x-72%29%29\"$ \n" ); document.write( "

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