I'll try to explain this, but it's hard to explain without knowing how much you know already.

For 2 and 3, the degree is the highest power of in the equation, so would have degree 5, and would still have degree 5.

Multiplicity would mean how many times a certain value is makes the equation equal to 0, so would have zeroes at 0 with multiplicity 2, whereas x would only have it with multiplicity 1. you can think of it as being able to factor out zeroes, so for it's the same as x*x, so there's two ways to get 0.

I'm assuming that you want real valued polynomials, so that means that for every complex number you get, it's conjugate is also a zero of the function. A complex number takes the form , and it's conjugate is just .

2.) degree 4: zeros: 3+2i; 4, mulpilicity 2

This means that you have 4 different factors from the degree, so you want to multiply together 4 things that have only degree equal to 1, so it's (x + a) (x+b)(x+c)(x+d) where a, b, c, d are all some value. Now we know that it has to zeroes at 4, so when you plug in 4 you get a 0, which only happens for (x-4). Since the multiplicity is 2, you have this two times. Te other zero is 3+2i, and it's conjugate must also be a zero, so you have 3+2i and 3-2i, which achieve zero at (x-3-2i) and (x-3+2i). Multiply these together: (x-4)(x-4)(x-3-2i)(x-3+2i) and you get your answer.