Answer :
[tex]\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)\\[/tex]
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.
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.