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

To determine the degree of the polynomial Q, we can use the property of polynomial division. According to the Polynomial Remainder Theorem, when a polynomial of degree n (in this case, P(x) of degree 5) is divided by another polynomial Q(x), the degree of Q(x) must be less than or equal to the degree of P(x).

Here, the remainder when P(x) is divided by Q(x) is 2x + 5, which is of degree 1. This implies that the degree of Q(x) cannot be greater than 1; otherwise, it would not be possible for the remainder to be of lower degree than both polynomials being divided. Therefore, we conclude:

• The degree of Q(x) could indeed be 1.