Let $P(x)$ be a polynomial of degree 5 - HSC - SSCE Mathematics Extension 1 - Question 3 - 2022 - Paper 1

To analyze the degree of the polynomial $Q(x)$, we can apply the polynomial remainder theorem. According to this theorem, when a polynomial $P(x)$ is divided by another polynomial $Q(x)$, the degree of $Q$ must be less than the degree of $P$ if there is a non-zero remainder.

In this case, since $P(x)$ is of degree 5 and the remainder, $2x + 5$, is of degree 1, it follows that the degree of $Q(x)$ could indeed be 2 or less. Thus, the correct option is:

D. The degree could be 2.