general Maths Puzzle

Find the reminder when x + x^3 + x^9 + x^27 + x^81 + x^243 is divided by (x^2 –1 )
a.6x b.4x c.6x+1 d.4x+1

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general Other Question

Let N = 10000!. N is divided successively by distinct numbers of the form xx where x is a prime number. What is the maximum number of divisions that can be performed, before getting a non-zero remainder?
a. 26 b. 25 c. 27 d. 28
When 7179 and 9699 are divided by another natural number N, remainder obtained is same. How many values of N will be ending with one or more than zeroes?
a.24 b.124 c.46 d.None of these