number of normed polynomials with degree d I am Arthur from Belgium student in 2nd year of mathematics and I am repeating the exercises for Algebra I, but this one extra exercise I just can't solve: 

14.
ii) If $\mathbf{F}$ is a finite field with $q$ elements, and $N_{d} = N_{d}(\mathbf{F})$ is the number of normed (monic) polynomials P in $\mathbf{F}[t]$ with degree d. What are $N_{2}$, $N_{3}$ ? 

If there is anybody who understands these exercise, I would be very glad if you could explain them to me. Because when my professor tried it, I don't seem to have understood. Thank you for your attention. 

You need to count the number of polynomials of degrees $2$ and $3$ respectively.
A normed polynomial of degree $2$ looks like this: $a_0 + a_1 x + x^2$. In how many ways can you choose $a_0$ and $a_1$? You have $q$ possibilities to choose $a_0$ and $q$ possibilities to choose $a_1$. How many polynomials do you get?
Now you do the same for polynomials of the form $a_0 + a_1 x + a_2 x^2 + x^3$.
