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\frac{x^{100}}{x^2-3x+2}\\ \\Quotient=x^{98}+3x^{97}+7x^{96}+15x^{95}+...\\\\=\Sigma_{n=0}^{98}\ (2^{n+1}-1)\ x^{98-n}\\ \\Remainder = (2^{100}-1)x-(2^{100}-2)\\

If you do the division step by step you will find that the quotient and reminder will be these values.  At the first division n = 0, and next division it is 1 and so on. The reminder is obtained when n=99 and after 99 successive divisions, until the reminder polynomial has an order of 1.

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