Need help with Factoring and Solving Equations.

Hi! Ive been trying to do these problems for a while and Im stumped. I finished 13 problems and fully understand them , but I don't know how to do these problems. It would be nice if you could write each step out or the answer at the very least. Or hints or tips, like which theorem or something to use. Shortcuts.

1. P(x) = 5x + 2kx^4 + 4x^3 - 5k

P(x)/2x+4 has a remainder of 3, find k.

2. f(x) = -2x^4 + ix^3 - 2kx^2 - x + 3

Find k given that (x + 1 + i) is a factor

I dont even know how to do 1 and 2.

is there any short cuts? (Crying)

Thanks for answering my questions. I really don't understand these problems. I mean I do, but I want to know shorter ways since everything takes so long.

I dont know when to use synthetic division, factor theorem, etc.

I need help

(Crying)