Hello MHF!

I have three questions that which are throwing me for a loop. While I understand some of the principals behind them, the questions themselves defy my ability to work out.

Q1:

Simplify:

$\displaystyle \frac{1}{2-i}$

(I have no idea where to begin to work this one out, or even if I have to...)

Q2:Find a quadratic equation with the roots (4+i) and (4-i).

(I have no idea where to start with this one either.......)

Q3:Use the factor theorem to determine whether (x-3) is a factor of $\displaystyle f(x)=x^4+12x^3+6x+27$

(I don't understand understand the Factor Theorem very well, so I find myself thoroughly lost.)

Many thanks in advance!