Question 1095133
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1. Factorise:  X^6 - 7X^3 - 8

   {{{x^6 - 7X^3 - 8}}} = {{{(x^3-8)*(x^3+1)}}} = {{{(x-1)*(X^2 + X + 1)*(X+1)*(X^2 - X + 1)}}}.



2. Find the factor for X^2 + 5&#8730;2x + 12



3. If x^11 + 101 is divided by x+1, then what is the reminder?

   The remainder is (-1)^11 + 101 = -1 + 101 = 100    (The remainder theorem).



4. Find value of polynomial x^2 - 9 for x=97

   It is  97^2 - 9 = (97+3)*(97-3) = 100*94 = 9400  (mental solution without a calculator).



5. if X^3 + 3X^2 + 3x + 1 is divided by x+1 then what is the {{{highlight(cross(reminder))}}}  remainder ?
 
   The remainder is  (-1)^3 + 3*(-1)^2 + 3*(-1) + 1 = -1 + 3 - 3 + 1 = 0.


   By the way,  X^3 + 3X^2 + 3x + 1 = (X + 1)^3.
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