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Kenny’s POTW Solution 3/29/10
When dividing x101+ x+ 1 by x2 + 1, look for a pattern.          X99 -x97 + x95-x93…                  x2+ 1  x101+ 0x100+0x99 … + x+1            -x101 –x100                     -x99 + 0x99 +x99 + x97        +x97 +0x98 -x97  - x95                               -x95…
The exponents of the answer are decreasing by two and switching signs every term. If you bring the pattern all the way down to terms that can work with the x + 1 in the dividend, you end up with… x3–x.  Taking this end of the answer, you can apply it to the end of the dividend. By using the opposite of x3 –x, you work backwards in the division like so…
           … x3 –x +1 x2+ 1  …x5 –x3 +x +1 -x5 – x3                  -x3 +x  +x3 +x 2x +1 ,[object Object]

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Kenny’S Potw Solution

  • 2. When dividing x101+ x+ 1 by x2 + 1, look for a pattern. X99 -x97 + x95-x93… x2+ 1 x101+ 0x100+0x99 … + x+1 -x101 –x100 -x99 + 0x99 +x99 + x97 +x97 +0x98 -x97 - x95 -x95…
  • 3. The exponents of the answer are decreasing by two and switching signs every term. If you bring the pattern all the way down to terms that can work with the x + 1 in the dividend, you end up with… x3–x. Taking this end of the answer, you can apply it to the end of the dividend. By using the opposite of x3 –x, you work backwards in the division like so…
  • 4.