In the following, all the operations and polynomials are defined over a finite field of prime order, $\mathbb{F}_p$, where $p$ is a sufficiently large prime number. All polynomials and values below are non-zero.
Let $F(x)= R(x)\cdot \phi(x)+Z(x)$, where the degree of each of the polynomials $R,Z$ and $\phi$ is $d>1$. Also, let $Z$ and $R$ be two polynomials picked uniformly at random from the field. Note $\phi$ is a fixed polynomial.
Question 1: Is $F(x)$ a MAC of $\phi$(x)?
Question 2: Is polynomial $\frac{F'(x)-Z(x)}{R(x)}$ a random polynomial distributed uniformly among polynomials of degree $d$ over $\mathbb{F}_p$? where $F'(x)$ is a fixed polynomial known by the adversary.