document.write( "Question 1044920: the remainder on division of x^5-x^4+x^3+2x^2-x+4 by x^3+1 is ? \n" ); document.write( "

Algebra.Com's Answer #660434 by josgarithmetic(39617) $\"\"$ $\"About$

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Polynomial division works the same way as regular base-ten division but often is easier.\r
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document.write( "             x^2    -x     1\r\n" );
document.write( "        _______________________________________________\r\n" );
document.write( "x^3+1   |    x^5   -x^4   x^3    2x^2    -x    4\r\n" );
document.write( "        |\r\n" );
document.write( "        |    x^5    0x^4  0x^3   x^2\r\n" );
document.write( "        -----------------------------\r\n" );
document.write( "              0    -x^4  x^3    x^2     -x\r\n" );
document.write( "                   -x^4  0x^3  0x^2    -x\r\n" );
document.write( "                  ------------------------\r\n" );
document.write( "                   0     x^3   x^2     0      4\r\n" );
document.write( "                         x^3   0x^2    0x     1\r\n" );
document.write( "                        ------------------------\r\n" );
document.write( "                          0   x^2      0     3\r\n" );
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document.write( "NOTE that the bottom row here shows degree 2, which is less than the degree 3 of the divisor!  Bottom row here represents the REMAINDER.\r\n" );
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\n" ); document.write( "Remainder is $\"x%5E2%2B3\"$ , which represents $\"%28x%5E2%2B3%29%2F%28x%5E3%2B1%29\"$ , just the way you would do if you were dividing plain base-ten numbers. \n" ); document.write( "

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