1) Multiply it by (1+2i) / (1+2i). Remember that i2 = -1. (1+2i) is the conjugate of the denominator.
2) Odd degrees have opposite end-behaviors: if one side goes up, the other goes down. Even degrees have the same end-behavior: if one side goes up so does the other, if one side goes down so does the other, It goes up for positive leading coefficients, down for negative.