document.write( "Question 252756: How is dividing a polynomial by a binomial similar or different from long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might uses polynomial division? \n" ); document.write( "
Algebra.Com's Answer #185102 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If you pick digits very carefully so there is\r\n" );
document.write( "no carrying to do in any of the multiplications or \r\n" );
document.write( "any borrowing to do in the subtractions, then you can \r\n" );
document.write( "create an example of long division of a polynomial\r\n" );
document.write( "by a binomial which is just like it, by using the digits\r\n" );
document.write( "as coefficientsl.\r\n" );
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document.write( "Here's an example of long division like we learned\r\n" );
document.write( "in elementary school that is just like a division\r\n" );
document.write( "by a binomial.\r\n" );
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document.write( "    4233                       4x^3 + 2x^2 + 3x + 3 \r\n" );
document.write( "  ------               ----------------------------\r\n" );
document.write( "21)88897         2x + 1)8x^4 + 8x^3 + 8x^2 + 8x + 7 \r\n" );
document.write( "   84                   8x^4 + 4x^3\r\n" );
document.write( "   --                   -----------\r\n" );
document.write( "    48                         4x^3 + 8x^2\r\n" );
document.write( "    42                         4x^3 + 2x^2\r\n" );
document.write( "    --                         -----------\r\n" );
document.write( "     69                               6x^2 + 9x\r\n" );
document.write( "     63                               6x^2 + 3x\r\n" );
document.write( "     --                               --------- \r\n" );
document.write( "      67                                     6x + 7\r\n" );
document.write( "      63                                     6x + 3\r\n" );
document.write( "      --                                     ------\r\n" );
document.write( "       4                                          4\r\n" );
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document.write( "Notice that the coefficients on the right are the same\r\n" );
document.write( "as the digits in the elementary school division on the\r\n" );
document.write( "left.  The difference is that in elementary school division,\r\n" );
document.write( "every number is considered to be positive, but that is not \r\n" );
document.write( "necessary in division of a polynomial by a binomial.  Also\r\n" );
document.write( "the coefficients don't have to be small enough to be digits,\r\n" );
document.write( "as they are here in the example above, in which I carefully\r\n" );
document.write( "selected the digits.  There is never any carrying or\r\n" );
document.write( "borrowing to do when dividing a polynomial by a binomial.\r\n" );
document.write( "Also in elementary school division, sometimes when you try\r\n" );
document.write( "a certain digit in the quotient it turns out to be too small \r\n" );
document.write( "or too large and then you have to erase it and make it larger \r\n" );
document.write( "or smaller as the case may be.  This is never required in \r\n" );
document.write( "division of a polynomial by a binomial.  But the two \r\n" );
document.write( "divisions in all other ways very similar.\r\n" );
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document.write( "Edwin
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