1.

Given the identity

$\displaystyle x^4 + x + 1$ = ($\displaystyle x^2+ A$)($\displaystyle x^2-1$) + Bx + C

determine the numerical value of A ,B and C. By giving x a suitable value, find the remainder when 100000101 is divided by 101.

I know how to do the first part, A is 1, B is 1 and C is 2, but don't know how to do part 2 which is in blue colour.

2.

Solve $\displaystyle 2^{-x}$$\displaystyle -2(2)^{-(x/2)+1}$ +3 =0

3.

Solve the equation

$\displaystyle log_{3}$(2x-3) = 2 - $\displaystyle log_{9}$$\displaystyle (2x-1)^2$