Question 204273
It  is  easy  to  divide a  polynomial  by (x+1),  however  with  exponents  of  100,  it  becomes  tedious,  as  all  exponents  must  be  "filled  in"  to  make  algorithm  work.
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However,  The  REMAINDER  THEOREM  states," if  a  polynomial,f(x) is divided by
(x-k),  the  remainder  is , r=f(k)"
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given  (x+1) = (x-k),,,k=(-1)
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To  find  remainder, evaluate, f(-1),  that  is  substitute  (-1) for (x)
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f(-1) = 3(-1)^100 +5(-1)^85 -4(-1)^38 +2(-1)^17 -6
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f(-1) = +3(1)+5(-1)-4(1) +2(-1) -6
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f(-1) = -14,,,,,and  REMAINDER = (-14)
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